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Andrew is designing a triangular bookcase for his friend. His blueprint shows that the bookcase is a right triangle with hypotenuse of length 14 meters, side length of *x* meters, and the other side length of 5 + *x* meters. What is the perimeter of the bookcase?

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Question:

A
33.16 meters

explanation

1212It is given that Andrew is dealing with a right triangle, so the Pythagorean theorem can be used to relate the side lengths to the hypotenuse. Substitute each value into the equation to produce an expression for *x*:
, which can be expanded to
, and rewriting as a quadratic
, which can be solved using the quadratic formula to give
x = -12.08 and x = 7.08
Notice that only 7.08 is a valid answer because side lengths cannot be negative. Also notice that it is the perimeter of the triangle that the question asks for:
7.08 + 5 + 7.08 + 14 = 33.16 meters.

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