SOLUTION: at a tennis club, a 1500 ft^2 rectangular area is partitioned into three rectangular courts of equal size. A total of 800 feet of fencing is used to enclose the three courts, incl

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Question 804220: at a tennis club, a 1500 ft^2 rectangular area is partitioned into three rectangular courts of equal size. A total of 800 feet of fencing is used to enclose the three courts, including the interior sides
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x and y dimensions.
x is divided into three equal lengths, so %281%2F3%29x.

Each court part is area %281%2F3%29xy, and the entire rectangular area for these court parts is xy=1500 ft%5E2.

Total fencing used is x%2By%2B2y=x%2B3y=800 ft.

The system is symbolically described with equations:
x%2B3y=800 and xy=1500.
Fence length equation allows x=800-3y. Substitute...
%28800-3y%29y=1500
800y-3y%5E2=1500
800y-1500-3y%5E2=0
-800y%2B1500%2B3y%5E2=0 when multiplied both sides by -1.
3y%5E2-800y%2B1500=0

General Solution to Quadratic Formula:
y=%28800%2Bsqrt%28800%5E2-4%2A3%2A%281500%29%29%29%2F%282%2A3%29
y=%28800%2Bsqrt%28622000%29%29%2F%282%2A3%29

scratchwork...8*77750=8*50*1555=8*50*5*311...
2*2*2*2*5*5*5*311...
sqrt(622000)=20*sqrt(5*311)...

y=%28800%2B20%2Asqrt%281555%29%29%2F%282%2A3%29
y=%28400%2B10%2Asqrt%281555%29%29%2F3 relatively simple radical form.

You can finish for finding x value.