A rectangular piece of carpet covers 10 yd^2. The width is 4 yd less than the length. Find the length and width.
1 answer:
Answer:
- length: 5.7 yd
- width: 1.7 yd
Step-by-step 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.
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