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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 18. Compute c.

 

 

 

 

thanks :D

 Apr 19, 2020
 #1
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Algebra will be our friend in this problem. We already have our variables to work with, so let's set up some equations:

 

\(6^2 + b^2 = c^2\) by Pythagorean theorem

We also have that the perimeter is 18, meaning:

\(6+b+c = 18\)

\(b+c = 12\)

\(b = 12-c\)

Substitute back into our equation from the Pythagorean theorem, and we can solve for the value of c.

\(6^2 + (12-c)^2 = c^2\)

\(36 + 144-24c + c^2 = c^2\)

\(180 -24c = 0\)

\(24c = 180\)

\(c = 180/24 = 30/4 = 15/2\)

.
 Apr 20, 2020

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