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# Right triangle

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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.

Apr 29, 2022

#1
+1351
+2

We have the following system:

\(6+b+c=24\)       (1)

\(36+b^2=c^2\)             (2)

Solve for \(c\) in the first equation: \(c=18-b\)

Squaring this gives \(b^2-36b+324\)

Substituting this in (2) gives: \(36+b^2=b^2-36b+324\)

Solving, we find that \(b= 8\)

Subsituting this in to (1), we find that \(\color{brown}\boxed{c = 10}\)

Apr 29, 2022
edited by BuilderBoi  Apr 29, 2022

#1
+1351
+2

We have the following system:

\(6+b+c=24\)       (1)

\(36+b^2=c^2\)             (2)

Solve for \(c\) in the first equation: \(c=18-b\)

Squaring this gives \(b^2-36b+324\)

Substituting this in (2) gives: \(36+b^2=b^2-36b+324\)

Solving, we find that \(b= 8\)

Subsituting this in to (1), we find that \(\color{brown}\boxed{c = 10}\)

BuilderBoi Apr 29, 2022
edited by BuilderBoi  Apr 29, 2022