Verified Answer :

Just use pythagorean theorem (a² + b² = c²)

We have a and c, so we need to find b:

a = 9 and c = 15 so

9² + b² = 15²

b² = 15²-9²

b² = 144

b = 12

So the missing side length of the triangle is 12 mm

Since it's a right angle, you can do the Pythagorean theorem backwards. Let's call the 9mm side A, the missing side B, and the longest side C.

\(a^{2} + b^{2} = c^{2}\)
\(9^{2} + b^{2} = 15^{2}\)
\(81 + b^{2} = 225\)
\(b^{2} = 225 - 81\)
\(b^{2} = 144\)
\(b = 12\)

The answer is 12mm