SOLUTION: The perimeter of a rectangle is 40 inches, and the area is 84 square inches. Find the length and width of the rectangle.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The perimeter of a rectangle is 40 inches, and the area is 84 square inches. Find the length and width of the rectangle.      Log On


   

Question 883362: The perimeter of a rectangle is 40 inches, and the area is 84 square inches. Find the length and width of the rectangle.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x and y dimensions.
Perimeter,2x+2y=40 simplifiable to x+y=20.
Area, xy=84.

Use substitution.
y=20-x.
x%2820-x%29=84.
-x%5E2%2B20x-84=0
highlight_green%28x%5E2-20x%2B84=0%29.

Discriminant: %28-20%29%5E2-4%2A84=64=8%5E2
Continue in the general solution for a quadratic equation:
x=%2820%2B8%29%2F2=14, guessing that the PLUS form should work and not the MINUS form.

y=20-14=6; but actually, either PLUS or MINUS form would work. One way would give 14 as found, and the other would give 6.
The dimensions are 14 and 6