# If the length of a rectangle is 3 feet less then twice its width and the area is 54square feet what are its dimensions

QUESTION POSTED AT 10/10/2019 - 07:35 PM

QUESTION POSTED AT 10/10/2019 - 07:35 PM

The length (L) of the rectangle can be written as a function of the width (W):

Now since we know Area = Width*Length, we can write the area as a function of the width:

Distributing the W inside the parentheses we have:

We know the area is 54 ft^2, so we can rewrite it as:

Now solve for W by factoring (or by applying the quadratic formula):

Factor out a common 2W from the first two terms and a 9 from the last two terms:

Regroup the terms to get our fully factored equation:

This gives us the roots W = 6 and W = -9/2, but width can't be negative so we have width = 6 ft. Then remember that the length L = 2W - 3, so our length is:

So now we know that our rectangle is 9 feet long and 6 feet wide.

Now since we know Area = Width*Length, we can write the area as a function of the width:

Distributing the W inside the parentheses we have:

We know the area is 54 ft^2, so we can rewrite it as:

Now solve for W by factoring (or by applying the quadratic formula):

Factor out a common 2W from the first two terms and a 9 from the last two terms:

Regroup the terms to get our fully factored equation:

This gives us the roots W = 6 and W = -9/2, but width can't be negative so we have width = 6 ft. Then remember that the length L = 2W - 3, so our length is:

So now we know that our rectangle is 9 feet long and 6 feet wide.

According to the image:

the right hexagonal pyramid surface area is given by the following formula:

S = 3√3 / 2) a² + 3a √h²+3a²/4

a = the base edge

h = the height of the pyramid

looking at the image a =6m, h =21m - 7m= 14m

so the surface area is S = 3√3 / 2) 6² + 3*6√14²+3*6²/4 =93.53+ 14.93=108.46 m²

for the another one

the figure is a prism hexagonal

its surface area is

SA= 6ah +3√3 a²

a= base edge, h =height

in our case a =6m and h = 7m

so SA= 6*6*7 + 3√3 * 6²= 252 + 187 = 439 m²

finally, the surface area of the complete image is

ST= S + SA = 108.46 m² + 439 m² = 547.52 m²

it is so approximate

to B. 615.53 m2

look at the image

the right hexagonal pyramid surface area is given by the following formula:

S = 3√3 / 2) a² + 3a √h²+3a²/4

a = the base edge

h = the height of the pyramid

looking at the image a =6m, h =21m - 7m= 14m

so the surface area is S = 3√3 / 2) 6² + 3*6√14²+3*6²/4 =93.53+ 14.93=108.46 m²

for the another one

the figure is a prism hexagonal

its surface area is

SA= 6ah +3√3 a²

a= base edge, h =height

in our case a =6m and h = 7m

so SA= 6*6*7 + 3√3 * 6²= 252 + 187 = 439 m²

finally, the surface area of the complete image is

ST= S + SA = 108.46 m² + 439 m² = 547.52 m²

it is so approximate

to B. 615.53 m2

look at the image

ANSWERED AT 17/10/2019 - 09:24 AM

QUESTION POSTED AT 17/10/2019 - 09:24 AM

*Answer: =50 *

*Explanation: An unknown leg of a right triangle can be found using the Pythagorean theorem. Pythagorean theorem: a²+b²=c²*

a²=14²+48²

a²=14²=14*14=196

a²=48²=48*48=2304

a²=196+2304

a²=196+2304=2500

a²=2500

a²=(25*100)=2500

a=5*10=50

*A=50*

*Hope this helps!*

*Thanks!*

*Have a great day!*

ANSWERED AT 17/10/2019 - 09:22 AM

QUESTION POSTED AT 17/10/2019 - 09:22 AM

The answer:

first, the angle of elevation, the shadow and the statue form an right triangle.

so, we know that for computing tangent, we use the main formula:

Tan = opposite side / adjacent side

let x be the length of the statue, it is the opposite side

30 feet long is the adjacent side

therefore,

tan50°= x /30, 1.19 * 30= x, and the x=35.75 feet

first, the angle of elevation, the shadow and the statue form an right triangle.

so, we know that for computing tangent, we use the main formula:

Tan = opposite side / adjacent side

let x be the length of the statue, it is the opposite side

30 feet long is the adjacent side

therefore,

tan50°= x /30, 1.19 * 30= x, and the x=35.75 feet

ANSWERED AT 17/10/2019 - 09:22 AM

QUESTION POSTED AT 17/10/2019 - 09:22 AM

We want to use the Pythagorean theorem to find the missing length of the right triangle described in the word problem.

The Pythagorean Theorem is a^2 + b^2 = c^2, where a and b are the side lengths of the right triangle, and c is the hypotenuse.

If we know the lengths of two sides of a triangle, we can always find the length of the third side using this formula.

We're given the lengths of one of the sides (12) and the hypotenuse (20). We plug these numbers into our equation and then solve for x.

(x represents the how high the ladder reaches)

x^2 + 12^2 = 20^2

x^2 + 144 = 400

x^2 + 144 - 144 + 400 - 144

x^2 = 256

Now, find the square root of each side of the parenthesis.

√x^2 = √256

x = 16.

The answer is 16.

If there's anything you don't understand, I would highly recommend going to the website Khan Academy and watch his videos regarding it, he explains things much better than I ever could.

Hope this helps!!

The Pythagorean Theorem is a^2 + b^2 = c^2, where a and b are the side lengths of the right triangle, and c is the hypotenuse.

If we know the lengths of two sides of a triangle, we can always find the length of the third side using this formula.

We're given the lengths of one of the sides (12) and the hypotenuse (20). We plug these numbers into our equation and then solve for x.

(x represents the how high the ladder reaches)

x^2 + 12^2 = 20^2

x^2 + 144 = 400

x^2 + 144 - 144 + 400 - 144

x^2 = 256

Now, find the square root of each side of the parenthesis.

√x^2 = √256

x = 16.

The answer is 16.

If there's anything you don't understand, I would highly recommend going to the website Khan Academy and watch his videos regarding it, he explains things much better than I ever could.

Hope this helps!!

ANSWERED AT 17/10/2019 - 09:20 AM

QUESTION POSTED AT 17/10/2019 - 09:20 AM

12 yards, 432 inches and 36 feet are all equal

12 yards = 36 feet

36 feet = 432 inches

12 yards = 36 feet

36 feet = 432 inches

ANSWERED AT 17/10/2019 - 09:15 AM

QUESTION POSTED AT 17/10/2019 - 09:15 AM

A trapezoid. It only has one pair of parallel sides, doesn't have four right angles and all sides are not the same length.

ANSWERED AT 17/10/2019 - 09:13 AM

QUESTION POSTED AT 17/10/2019 - 09:13 AM

The surface area of a rectangular prism is:

A=2(xy+xz+yz), where x,y, and z are its dimensions...in this case:

A=2(120*110+120*4+110*4)

A=2(13200+480+440)

A=2(14120)

A=28240 mm^2

A=2(xy+xz+yz), where x,y, and z are its dimensions...in this case:

A=2(120*110+120*4+110*4)

A=2(13200+480+440)

A=2(14120)

A=28240 mm^2

ANSWERED AT 17/10/2019 - 09:11 AM

QUESTION POSTED AT 17/10/2019 - 09:11 AM

surface area is the area of all the faces on a shape so to speak.

2(120 x 110)=26,400

2(120 x 4)=960

2(110 x 4)=880

880+960+26,400=28,240

Surface area = 28,240

ANSWERED AT 17/10/2019 - 09:11 AM

QUESTION POSTED AT 17/10/2019 - 09:11 AM

Point D is the midpoint of the outer circle that we aim to find the area of

The circle has a diameter of WZ and radii of WC and CZ

We know that YZ=YD=10 cm

Let DC be and CY be

The radius of the outer circle can be written as or which we can equate to find the value of

Therefore, the radius of the circle is

And hence the area of the circle is =324

The circle has a diameter of WZ and radii of WC and CZ

We know that YZ=YD=10 cm

Let DC be and CY be

The radius of the outer circle can be written as or which we can equate to find the value of

Therefore, the radius of the circle is

And hence the area of the circle is =324

ANSWERED AT 17/10/2019 - 09:07 AM

QUESTION POSTED AT 17/10/2019 - 09:07 AM

the answer is 3/8 that's the answer to the problem

ANSWERED AT 17/10/2019 - 09:07 AM

QUESTION POSTED AT 17/10/2019 - 09:07 AM

It should be 10 cm thanks

ANSWERED AT 17/10/2019 - 09:06 AM

QUESTION POSTED AT 17/10/2019 - 09:06 AM

Volume formulas:

rectangle prism: l×w×h

cube: s^3

cylinder:(pi)r^2×h

triangle prism: (a×b/2)×h

cylinder:(pi)r^2×h

box:l×w×h

40) 5m×3m×4m =15m×4m= 60m^3

41) 6 ft × 6 ft ×6 ft = 36 ft × 6 ft = 216 ft^3

42) d=2r 10/2=5 r=5

3.14×5^2×14=78.5×14= 1099cm^3

43) 15=a×b/2 (area of trianlge)

15×12= 180in^3

44) c=2 (pi)r 8pi=2r (pi)

r=4

3.14×4^2×7=50.24×7=351.68

45) 24 ft^3 =2 ft × 3 ft × height

24=6×h

÷6 both sides

h=4ft

rectangle prism: l×w×h

cube: s^3

cylinder:(pi)r^2×h

triangle prism: (a×b/2)×h

cylinder:(pi)r^2×h

box:l×w×h

40) 5m×3m×4m =15m×4m= 60m^3

41) 6 ft × 6 ft ×6 ft = 36 ft × 6 ft = 216 ft^3

42) d=2r 10/2=5 r=5

3.14×5^2×14=78.5×14= 1099cm^3

43) 15=a×b/2 (area of trianlge)

15×12= 180in^3

44) c=2 (pi)r 8pi=2r (pi)

r=4

3.14×4^2×7=50.24×7=351.68

45) 24 ft^3 =2 ft × 3 ft × height

24=6×h

÷6 both sides

h=4ft

ANSWERED AT 17/10/2019 - 09:06 AM

QUESTION POSTED AT 17/10/2019 - 09:06 AM

The shorter piece would be 3 feet long and the longer piece would be 9 feet long.

ANSWERED AT 17/10/2019 - 09:04 AM

QUESTION POSTED AT 17/10/2019 - 09:04 AM

The shaded region is the area of the circle minus the area

of the pentagon.

A circle = pi * r^2

A circle = pi * 15^2

A circle = 706.5 cm^2

A regular pentagon = (a * p)/2 where a is the apothem, p is the perimeter.

The apothem id the perpendicular height from the midpoint of a side to the center of the pentagon.

To find the apothem you have to use a trig ratio.

A pent = (8.3 * 12*5)/2

A pent = 249 cm^2

Shaded region: circle - pentagon 706.5 - 249 = 457.5

of the pentagon.

A circle = pi * r^2

A circle = pi * 15^2

A circle = 706.5 cm^2

A regular pentagon = (a * p)/2 where a is the apothem, p is the perimeter.

The apothem id the perpendicular height from the midpoint of a side to the center of the pentagon.

To find the apothem you have to use a trig ratio.

A pent = (8.3 * 12*5)/2

A pent = 249 cm^2

Shaded region: circle - pentagon 706.5 - 249 = 457.5

ANSWERED AT 17/10/2019 - 09:04 AM

QUESTION POSTED AT 17/10/2019 - 09:04 AM

3ft x 14ft = 42ft^2

240ft^2

-------

42ft^2

5.7

ANSWERED AT 17/10/2019 - 09:02 AM

QUESTION POSTED AT 17/10/2019 - 09:02 AM

**Answer:**

45

**Step-by-step explanation:**

ANSWERED AT 17/10/2019 - 09:02 AM

QUESTION POSTED AT 17/10/2019 - 09:02 AM

Answer: 11 and 9

Step-by-step explanation:

ANSWERED AT 17/10/2019 - 09:01 AM

QUESTION POSTED AT 17/10/2019 - 09:01 AM

Bear in mind that, a square is just a rectangle with all equal sides, thus, if say one side is length "x", all sides are "x" long then

check the picture below

check the picture below

ANSWERED AT 17/10/2019 - 09:01 AM

QUESTION POSTED AT 17/10/2019 - 09:01 AM

THE CORRECT ANSWER IS 25

ANSWERED AT 17/10/2019 - 08:59 AM

QUESTION POSTED AT 17/10/2019 - 08:59 AM

Pythagorean Theorem. Right triangles only!

ANSWERED AT 17/10/2019 - 08:50 AM

QUESTION POSTED AT 17/10/2019 - 08:50 AM

6 3/4 feet

2 1/4+2 1/4+ 2 1/4= 6 3/4

2 1/4+2 1/4+ 2 1/4= 6 3/4

ANSWERED AT 17/10/2019 - 08:49 AM

QUESTION POSTED AT 17/10/2019 - 08:49 AM

see the attached figure to better understand the problem

we know that

-------> equation

-------> equation

equate equation and equation

therefore

__the answer is__

ANSWERED AT 17/10/2019 - 08:49 AM

QUESTION POSTED AT 17/10/2019 - 08:49 AM

The answer to the problem is a

ANSWERED AT 17/10/2019 - 08:47 AM

QUESTION POSTED AT 17/10/2019 - 08:47 AM

The answer is actually 7. I took the test.

ANSWERED AT 17/10/2019 - 08:38 AM

QUESTION POSTED AT 17/10/2019 - 08:38 AM

The scale length is 9cm and the scale is 6cm/15ft which is 3cm/5ft, so we can say:

9cm(5ft/3cm)=15ft for the length

If you wanted the width too...

4cm(5ft/3cm)=20ft/3 (6'8", 6ft 8in)

9cm(5ft/3cm)=15ft for the length

If you wanted the width too...

4cm(5ft/3cm)=20ft/3 (6'8", 6ft 8in)

ANSWERED AT 17/10/2019 - 08:34 AM

QUESTION POSTED AT 17/10/2019 - 08:34 AM

A Pythagorean Triplet is simply when all sides are integers, so we can check what x would be if it were the hypotenuse...

x^2=20^2+21^2

x^2=400+441

x^2=841

x=√841

x=29

x^2=20^2+21^2

x^2=400+441

x^2=841

x=√841

x=29

ANSWERED AT 17/10/2019 - 08:30 AM

QUESTION POSTED AT 17/10/2019 - 08:30 AM

Percent increase = 36-30/30 x 100

percent increase = 6/30 x 100

20 percent

percent increase = 6/30 x 100

20 percent

ANSWERED AT 17/10/2019 - 08:29 AM

QUESTION POSTED AT 17/10/2019 - 08:29 AM

A=side

b=base

γ=gamma

A=a b

A=50*20*

A≈482.96 m^2

b=base

γ=gamma

A=a b

A=50*20*

A≈482.96 m^2

ANSWERED AT 17/10/2019 - 08:25 AM

QUESTION POSTED AT 17/10/2019 - 08:25 AM

**Answer:**

**Option B. 1134.16 cm³**

**Step-by-step explanation:**

The surface area of two similar solids are 1,008 cm² and 1372 cm²

Since surface area is a two dimensional unit or surface area is the multiplication of two dimensions.

Ratio of the sides of the solids will be

Ratio of sides =

= 1.167

Now ratio of volume of the solids will be cube of the sides.

=

By cross multiplication

V(1.167)³ = 1801

V = = 1134.16 cm³

Option B. 1134.16 cm³ is the answer.

ANSWERED AT 17/10/2019 - 08:24 AM

QUESTION POSTED AT 17/10/2019 - 08:24 AM

**Answer:**

The required formula is .

**Step-by-step explanation:**

The given equation is

where,

1. f is the focal length of the lens.

2. p is the distance of the object from the lens.

3. q is the distance of the image from the lens.

We have to rearrange the formula for q.

Multiply both sides by fpq.

Subtract fq from both the sides.

Take out the common factor q.

Divide both the sides by (p-f)

Therefore the required formula is .

ANSWERED AT 17/10/2019 - 08:22 AM

QUESTION POSTED AT 17/10/2019 - 08:22 AM