SOLUTION: The perimeter of a rectangular floor is 42 feet, and the area is 108 square feet. Find the length of the floor.

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Question 4268: The perimeter of a rectangular floor is 42 feet, and the area is 108 square feet. Find the length of the floor.
Answer by Earlsdon(6287) About Me  (Show Source):
You can put this solution on YOUR website!
Assign the variables: L = length, W = width.
Perimeter = 2(L+W) = 42 ft. or L+W = 21 ft. Rewrite as: W = 21-L and substitute into the area equation.
Area = L*W = 108 sq.ft.
L(21-L) = 108
21L - L^2 = 108 Rewrite as standard quadratic equation:
L^2 - 21L + 108 = 0 Solve by factoring:
(L - 12)(L - 9) = 0 Apply the zero products principle:
L - 12 = 0, L = 12 or L - 9 = 0, L = 9
These two roots of the quadratic are the Length and the Width. You can arbitrarily choose the longer one for the length, although mathematically it doesn't make any difference which one you call the length or the width.
Length of floor is 12 ft.
Check: Perimeter: P = 2(L+W) = 2(12+9) = 2(21) = 42 ft.
Area: A = L*W = 12*9 = 108 sq. ft.