You are correct in the first part of the equation:
But your second equation is wrong. The area of a rectangle is base * height... so where did you get the x^2 and y^2 from?
The equation for the area should be:
Now that we have 2 equations with 2 variables, we can use simultaneous equation to solve for x and y, the dimensions of the playground.
First equation: which if we rewrite in the form of y= , we get
Now we substitute from the first equation of y = 216/x into the second equation whenever y occurs. This leaves us with:
Multiply everything by x to make it easier to solve:
Now solve the equation for x, using the quadratic formula or by factorising. You should get 2 answers, and those are the dimensions of the playground.