quadratic question

Question

A carpet is 7 yards longer than it is wide. If it has an area of 21 square yards, what are its dimensions? Round your results in yards to one decimal place. Suggestion: Refer to the figure below, where x is in yards. Use the dimensions shown in that figure to calculate the area, and set that equal to 21 square yards.
width
yd
length
yd

Answer 1

There was no figure below.

Let w = the width

Let w + 7 = the length

A = lw

21 = w(w + 7)

21 = w² + 7w

w² + 7w - 21 = 0     Use the quadratic formula.

 

w = -7 ± √[7² - 4(1)(-21)]

                 2(1)

w = -7 ± √(49 + 84)

                  2

w = -7 ± √133

              2

w = -7 ± 11.53256

              2

w ≈ 2.3 yards

length = w + 7 ≈ 9.3 yards