The length of a rectangle is 4 centimeters less than twice its width. The perimeter of the rectangle is 34 cm. What are the dimensions of the rectangle?

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bentleytj21yourmom bentleytj21yourmom

03-03-2016
Mathematics

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The length of a rectangle is 4 centimeters less than twice its width. The perimeter of the rectangle is 34 cm. What are the dimensions of the rectangle?

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Munchkinmas23 Munchkinmas23 · Answer 1 · 2016-03-03T19:01:37+01:00

Let L=length and W=Width.

The length of a rectangle is 4 centimeters less than twice its width.

This would mean that:
L= 2w-4

To find the perimeter of a rectangle you add all sides together. This would be shown as 2L+2W

Therefore, 2L+2W= 34

Since this equation has two unknowns, you cannot solve it; but we know that L=2W-4

So if we substitute that into the equation of the perimeter, you would get:
2(2W-4)+2W=34.

This only has one unknown so we can solve it. Here are the steps:

2(2W-4)+2W=34
4W-8+2W=34
6W-8=34
6W=42
W=7

Now that we know what W is we can work out L.

L=2W-4
L=14-4
L=10

So W=7 and L=10!

This shows that the length is 10cm and the width is 7cm.

I hope this helped!