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Gemiola [76]
3 years ago
9

The ratio of the width to the length of a rectangle is 3:7. The shorter side is 9 inches long. What is the longer side and also

the area of the rectangle? Please show your work.
Mathematics
2 answers:
photoshop1234 [79]3 years ago
3 0

shorter side : longer side = 3 : 7


Equate 3 parts tp 9 inches:

3 parts = 9 inches


Find 1 part:

1 part = 9 ÷ 3 = 3 inches


Find 7 parts:

7 parts = 3 x 7 = 21 inches


Area = Length x Width = 21 x 9 = 189 in²


Answer: The longer side is 21in and the area is 189 in²

andreyandreev [35.5K]3 years ago
3 0
Take the length of the shortest side divide that by the ratio of the shortest side 9/3 =3

Take that number 3 and multiply it by seven.
3*7=21

The shorter side is 9 inches, and the longer side is 21 inches.

To find the area, multiply 21 by 9.
The area is 189 inches
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=====================================================

Work Shown:

I have attached two images below. The first shows figures 1 through 4. The second image shows figure 5.

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The green portions in figures 3 and 4 indicate where the flaps used to be in reference to figure 2.

-------------------

Since those dashed lines in figure 1 were x inches long, this means that the distance from A to B is 11-x-x = 11-2x inches long.

This makes segment BD to be 8-2x inches long. We are subtracting off 2 copies of x each time for each dimension.

------------------

length = AB = 11-2x

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The restriction 0 < x < 4 will be used later.

------------------

For now, let's compute the volume.

Volume = Length*Width*Height

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Volume = (11-2x)*(8-2x)*x

Volume = (88-22x-16x+4x^2)*x

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