MATH SOLVE

3 months ago

Q:
# 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.

Accepted Solution

A:

Answer:length: 5.7 ydwidth: 1.7 ydStep-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 . . . yardsThe length and width are 5.7 and 1.7 yards, respectively._____In the attached graph, we let x represent the length. As you can see, the magnitudes of the two zeros are width and length.