The area of a rectangular carpet is 27 27 square feet. The length is six feet more than the width. Find the length and the width of the carpet.

Question

The area of a rectangular carpet is  square feet. The length is six feet more than the width. Find the length and the width of the carpet.

Answer 1

For a rectangle

Area = Length x Width

A = L x W

A = 27 ft²

L = W + 6

A = W(W + 6)

27 = W² + 6W

A quadratic can be applied here, subtract 27 from both sides

0 = W² + 6W - 27

Factoring

(W + 9)(W - 3) = 0

W cannot be negative 9 so W = 3

Substituting, according to information given

L = 3 + 6 = 9

Length = 9 ft

Width = 3 ft

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