Question

triangle xyz is a right triangle with legs measuring 8 cm and 15 cm. what is the length of xz?

Explanation:

Step1: Recall Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the legs and \(c\) is the hypotenuse. Here \(a = 8\) cm, \(b = 15\) cm, and we want to find the hypotenuse \(XZ\).
\[XZ=\sqrt{8^{2}+15^{2}}\]

Step2: Calculate squares

First, calculate \(8^{2}=64\) and \(15^{2}=225\).
\[XZ=\sqrt{64 + 225}\]

Step3: Add values under square - root

\[64+225 = 289\]
\[XZ=\sqrt{289}\]

Step4: Find square - root

\(\sqrt{289}=17\)

Answer:

17 cm