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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 24. Compute c.

 Nov 26, 2020

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 #2
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 Firstly, we write \(b^2+36=c^2\). Then, we write \(b+c=18\). These are from the two given conditions. We manipulate the first equation to \((b+c)(b-c)=-36\). Plugging in our value, we find that \(b-c=-2\). Therefore, \(b=8, c=\boxed{10}\).

 Nov 26, 2020
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triangle 6-8-10

 Nov 26, 2020
 #2
avatar+110 
+1
Best Answer

 Firstly, we write \(b^2+36=c^2\). Then, we write \(b+c=18\). These are from the two given conditions. We manipulate the first equation to \((b+c)(b-c)=-36\). Plugging in our value, we find that \(b-c=-2\). Therefore, \(b=8, c=\boxed{10}\).

OlympusHero Nov 26, 2020

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