Question

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

Explanation:

Step1: Find the base $b$ using Pythagorean theorem

By the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 5.4$ cm and $a = 4.7$ cm. So $b=\sqrt{c^{2}-a^{2}}=\sqrt{5.4^{2}-4.7^{2}}=\sqrt{(5.4 + 4.7)(5.4 - 4.7)}=\sqrt{10.1\times0.7}=\sqrt{7.07}\approx2.7$ cm.

Step2: Calculate the perimeter $P$

The perimeter of a triangle $P=a + b + c$. Substitute $a = 4.7$ cm, $b\approx2.7$ cm and $c = 5.4$ cm. So $P=4.7+2.7 + 5.4=12.8$ cm.

Answer:

$12.8$