Question

The width of a rectangle is 3 3 feet longer than two times its length, and its area is 27 27 . If you use L L to represent the length of the rectangle, then an expression representing the width is W

Answer 1

Expression representing the width,W, = 3 + 2L

Lenght is 3 feet

Width is 9 feet

Explanation:

Please refer to the attached image for explanations

Answer 2

The expression representing the width is 3+2L

The width is 9ft

Explanation:

Area of a rectangle = Length×width

A = L × W...(1)

Let the length be represented as L

Since the width of the rectangle is 3feet longer than two times its length, this is expressed as:

First, width is twice as long as the length i.e W = 2L

If the resulting width is now 3 feet longer, the final width of the rectangle will be expressed as:

W = 3+2L...(2)

Area (A) = 27ft

Substituting equation 2 into 1, we have;

A = L(3+2L)

A = 3L+2L²

27 = 3L+2L²

2L²+3L-27 = 0

Factorizing the resulting equation

(2L²+9L)-(6L-27) = 0

L(2L+9)-3(2L+9) = 0

L-3 = 0 and 2L+9 = 0

L = 3 and L = -9/2

Disregarding the negative value and substituting L = 3 into equation 2 to get the width

W = 3+2(3)

W = 3+6

W = 9ft