Question

5.4 cm, 4.7 cm, b (right triangle). what is the perimeter? if necessary, round to the nearest tenth. centimeters

Explanation:

Step1: Find the length of \( b \)

This is a right - triangle, so we can use the Pythagorean theorem \( a^{2}+b^{2}=c^{2} \), where \( c = 5.4\) cm, \( a = 4.7\) cm. We need to solve for \( b \). Rearranging the formula gives \( b=\sqrt{c^{2}-a^{2}} \). Substitute \( c = 5.4\) and \( a = 4.7\) into the formula: \( b=\sqrt{5.4^{2}-4.7^{2}}=\sqrt{(5.4 + 4.7)(5.4 - 4.7)}=\sqrt{10.1\times0.7}=\sqrt{7.07}\approx2.66\) cm.

Step2: Calculate the perimeter

The perimeter \( P\) of a triangle is the sum of its three sides. So \( P=5.4 + 4.7 + b\). Substitute \( b\approx2.66\) into the formula: \( P=5.4+4.7 + 2.66=12.76\approx12.8\) cm.

Answer:

\(12.8\)