Question

A rectangular piece of carpet covers 10 yd^2. The width is 4 yd less than the length. Find the length and width.

Round your answers to the nearest tenth of a yard.

Answer 1

• length: 5.7 yd
• width: 1.7 yd

Explanation:

Let w represent the width of the carpet. Then the length is w+4 and the area is ...

w(w +4) = 10

w² +4w = 10 . . . . . eliminate parentheses

w² +4w +4 = 14 . . . . . . add the square of half the w-coefficient to complete the square

(w +2)² = 14 . . . . . . . . . rewrite as a square

w +2 = √14 . . . . . . . . . take the square root

2 = -2 +√14 ≈ 1.7 . . . . yards (width)

Then the length is 4 more yards than this, so is ...

length = 1.7 +4 = 5.7 . . . yards

The length and width are 5.7 and 1.7 yards, respectively.

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In the attached graph, we let x represent the length. As you can see, the magnitudes of the two zeros are width and length.