Mr. Yancey is building a fence around his square backyard. He bought materials to build 450 feet of fencing. The area of the yard is 21,780 square feet. Mr. Yancey will need to enclose three sides of his backyard.

Write an equation to represent the area of the backyard. Use s to represent the length of one side of the backyard.
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Determine if the amount of materials Mr. Yancey has purchased is enough to enclose his backyard on all three sides. Justify your answer using mathematical reasoning.

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The question is not exactly as clear as it could be. The square shape must have 4 sides. We must assume that the 4th side is a building, but it sure is big.

However working with what we have, 450 has to be cut into 3 parts. 450 / 3 = 150

So each side of fencing has to be 150

Area =s^2

s = 150

Area = 150^2

Area = 22500 square feet.

That's slightly bigger than 21780. What should be the size of the fence sides?

Take the square root of 21780 which is 147.6

That will be the size of each side of the 3 sides needed.