Question

A rectangular yard has area 96 square feet. If the width of the yard is 4 ft less than length, what is the perimeter,in feet, of the yard?

Answer 1

Area of the rectangular yard = 96 square feet
Let us assume the length of the yard = x feet
Width of the yard = x - 4 feet
Then
Area of the yard = length * width
96 = x(x - 4)
96 = x^2 - 4x
x^2 - 4x - 96 = 0
x^2 - 12x + 8x - 96 = 0
x(x - 12) +8(x - 12) = 0
(x - 12)(x + 8) = 0
As the value of length cannot be negative so
x - 12 = 0
x = 12
So
Length of the yard = 12 feet
Width of the yard = x - 4 feet
                             = 12 - 4 feet
                             = 8 feet
Then
Perimeter of the yard = 2 (length + width)
                                   = 2(12 + 8)
                                   = 2 * 20 feet
                                   = 40 feet.
So the perimeter of the yard  is 40 feet.