Question

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

Explanation:

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

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 9.4\) (hypotenuse) and \(b=6.9\). Then \(a=\sqrt{c^{2}-b^{2}}=\sqrt{9.4^{2}-6.9^{2}}=\sqrt{(9.4 + 6.9)(9.4 - 6.9)}=\sqrt{16.3\times2.5}=\sqrt{40.75}\approx6.4\)

Step2: Calculate the perimeter

The perimeter \(P\) of a triangle is \(P=a + b+ c\). Substitute \(a\approx6.4\), \(b = 6.9\), and \(c = 9.4\) into the formula. \(P=6.4+6.9 + 9.4=22.7\)

Answer:

\(22.7\)