Question

The length of a rectangle exceeds its width by 5
inches, and the area is 14 square inches. What
are the length and width of the rectangle?
Separate the answers with a comma.

Answer 1

Answer:

• 2 in and 7 in

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Let the length be l and width be w.

We are given that:

• 1) l = w + 5
• 2) lw = 14 (area is the product of length and width)

Substitute w + 5 for l into second equation:

• w(w + 5) = 14
• w² + 5w = 14
• w² + 5w - 14 = 0
• w² + 7w - 2w - 14 = 0
• w(w + 7) - 2(w + 7) = 0
• (w + 7)(w - 2) = 0
• w = - 7 or w = 2

The first root is discarded as negative.

So the width is 2 in, then the length is:

• l = 2 + 5
• l = 7 in