SOLUTION: The perimeter of a rectangle is 64 meters and its area is 253m^2. Find the dimensions of the rectangle.

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Question 911088: The perimeter of a rectangle is 64 meters and its area is 253m^2. Find the dimensions of the rectangle.
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
Unknown dimensions, x and y;
Given p perimeter and A area.

system%28A=xy%2Cp=2x%2B2y%29
2y=p-2x
y=%28p-2x%29%2F2
Substitute this into A equation.
xy=A
x%28p-2x%29%2F2=A
px-2x%5E2=2A
px-2x%5E2-2A=0
-2x%5E2%2Bpx-2A=0
2x%5E2-px%2B2A=0
x=%28p%2B-sqrt%28p%5E2-4%2A2%2A2A%29%29%2F%282%2A2%29
guessing that the PLUS square root form will be wanted,
highlight%28x=%28p%2Bsqrt%28p%5E2-16A%29%29%2F4%29

The easiest way to continue is to substitute for the given values for p and A and evaluate x.
Find y using what you found for the value of x, any equation found to be convenient;
maybe directly in y=A%2Fx.

p=64, and A=253.

x=%2864%2Bsqrt%2864%5E2-16%2A253%29%29%2F4
x=%2864%2Bsqrt%2848%29%29%2F4
x=%2864%2B4%2Asqrt%283%29%29%2F4
highlight%28x=16%2Bsqrt%283%29%29---one of the dimensions

y=253%2Fx
y=253%2F%2816%2Bsqrt%283%29%29
y=%28253%2F%2816%2Bsqrt%283%29%29%29%2816-sqrt%283%29%29%2F%2816-sqrt%283%29%29
y=%28253%2816-sqrt%283%29%29%29%2F%2816%5E2-3%29
y=%28253%2816-sqrt%283%29%29%29%2F253
highlight%28y=16-sqrt%283%29%29----other dimension