Question

find the missing side length, z.
12
9
z
13
15
16
18

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(a = 9\), \(b = 12\), and \(c=z\).
So, \(z^{2}=9^{2}+12^{2}\).

Step2: Calculate squares

\(9^{2}=81\), \(12^{2}=144\). Then \(z^{2}=81 + 144\).

Step3: Sum and find square root

\(z^{2}=225\). Taking square root, \(z=\sqrt{225}\).

Answer:

\(15\)