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The length of a rectangular rug is 4 less than twice its width. The perimeter of the rug is 34 feet. What is the area?

Sagot :

My first step is always to draw a picture

We are told the length is 4 less than twice the width

l = 2w-4

We are told the perimeter is 34

P =2(l+w)

Substitute the first equation in for l

P = 2( 2w-4 + w)

Combine like terms

34 = 2( 3w-4)

Distribute the 2

34 = 6w -8

Add 8 to each side

34+8 = 6w-8+8

42 = 6w

Divide by 6

42/6 = 6w/6

7 =w

Now we can find l

l = 2w-4 = 2(7) -4 = 14-4 = 10

The question asks for the area

A = l*w = 10 *7 = 70

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