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The area of a garden is 972 square feet, and the length of its diagonal is 45 feet.
Find the dimensions of the garden.
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The solution by @Mananth is irrelevant and has nothing in common with the problem.
For your safety, simply IGNORE HIS (or her) POST.
I came to bring the correct solution.
Notice how I edited the condition in order for the problem would make sense.
Let x be the larger dimension of the rectangle,
and let y be its smaller dimension.
Then we have these two equations from the condition
xy = 972 (1)
= 45. (2)
From equations (1) and (2), you get
x^2 + 2xy + y^2 = + 2*972 = 3969 =
x^2 - 2xy + y^2 = - 2*972 = 81 = .
It can be simplified to
x + y = 63
x - y = 9
It implies 2x = 63+ 9 = 72; x = 36; y = 27.
ANSWER. The dimensions of the rectangle are 36 feet and 27 feet.
Solved (correctly).