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A right triangle has legs of length 6 and b, and a hypotenuse of length c. The perimeter of the triangle is 15. Compute c.

 May 15, 2022
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By Pythagorean theorem, \(6^2 + b^2 = c^2\).

Perimeter is 15 means \(6 + b + c = 15\).

 

Then \(\begin{cases}c^2 - b^2 = 36\\b + c = 9\end{cases}\). Note that c^2 - b^2 = (c - b)(b + c) = 9(c - b). Therefore:

\(9(c - b) = 36\\ c - b = 4\)

 

Consider \(2c = (b + c) + (c - b)\).

 

\(2c = 9 + 4\\ c = \dfrac{13}2\)

 May 15, 2022

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