Question

what is the perimeter? if necessary, round to the nearest tenth. inches

Explanation:

Step1: Find the length of the unknown side \(a\)

Use the Pythagorean theorem \(a=\sqrt{c^{2}-b^{2}}\), where \(c = 9.4\) (hypotenuse) and \(b=6.9\) (one - leg).

$$a=\sqrt{9.4^{2}-6.9^{2}}=\sqrt{(9.4 + 6.9)(9.4 - 6.9)}=\sqrt{16.3\times2.5}=\sqrt{40.75}\approx6.4$$

Step2: Calculate the perimeter \(P\)

The perimeter of a triangle \(P=a + b + c\). Substitute \(a\approx6.4\), \(b = 6.9\), and \(c = 9.4\).

$$P=6.4+6.9+9.4=22.7$$

Answer:

\(22.7\)