Question

The width of a rectangle is 10 feet shorter than its length. The area of the rectangle is 60 square feet. Find the length and width. Round your answer to the nearest tenth of a foot.

Answer 1

Answer:

  length: 14.2 ft; width 4.2 ft.

Step-by-step explanation:

Let x represent the length of the rectangle in feet. Then x-10 represents the width, and the area is ...

  area = length×width

  60 = x(x -10) . . . . . substitute the expressions for area, length, width

  60 = x² -10x

  85 = x² -10x +25 . . . . add (10/2)² to complete the square

  85 = (x -5)² . . . . . . . . . rewrite as a square

  √85 = x -5 . . . . . . . . . take the square root. Only the positive root is useful for this problem

  x = 5 + √85 ≈ 14.2

  x-10 = 4.2

The length and width of the rectangle are 14.2 ft and 4.2 ft.