the area of a rug is 66 square ft. the length of the rug is 5 ft longer than the width. what is the width of the rug?

Question

the area of a rug is 66 square ft. the length of the rug is 5 ft longer than the width. what is the width of the rug?

Answer 1

First set up the area equation. LW = 66

 

Given L = W + 5

 

Substitute for L  (W + 5)W = 66

 

Distribution property W^2 + 5W = 66

 

Subtract 66 to both sides W^2 + 5W - 66 = 66 - 66

W^2 + 5W - 66 = 0

 

Factor (W - 6)(W + 11) = 0 since third term was negative, one factor must positive and the other negative whose sum equals the middle. 11 - 6 = 5

 

Only (W - 6)  is needed since (W + 11 ) will result in a negative answer.

 

Set to 0 W - 6 = 0 

 

Add 6 to both sides W - 6 + 6 = 0 + 6

W = 6

 

The width of the rug is 6ft.

 

Only positive answers are used if measurement problems.

 

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