Problema Solution
A rectangle has an area of 32 square feet and a perimeter of 24 feet. What is the shortest of the side lengths, in feet, of the rectangle?
Answer provided by our tutors
You set up the equations according to the formulas A = LW and P = 2L + 2W. (L = length, W = Width)
A = 32 = LW
P = 2L + 2W = 24
Solve for one of the variables.
2L + 2W = 24
2L = 24 - 2W
L = 12 - W
Plug it into the equation A = LW = 32. ---> (12 - W)W = 32, distribute the W ---> 12W - W^2 = 32.
You now have a quadratic equation and you solve for W. You get W = 4 and 8. The shortest side lengths are 4 and 8 units.