Question

1. Do you the following side lengths form a right triangle?2. Which measurement is closest to the value of X in centimeters?

Answer 1

Answer:

Part 1:

Yes, the side lengths form a right triangle.

Part 2:

Option d 37.1 cm

Explanation:

We need to use the pythagorean theorem.

In part 1, if the 3 side lengths are a right triangle, then, they must verify:

$7.5^2=4.5^2+6^2$

By the theorem. Then:

$\begin{gathered} 7.5^2=56.25 \\ 4.5^2+6^2=20.25+36=56.25 \end{gathered}$

They're equal, then the lengths correspond to a right triangle.

For part 2, we need to use again the theorem. In this case:

$\begin{gathered} 12^2+x^2=39^2 \\ x=\sqrt{1521-144} \\ x=\sqrt{1377} \\ x\approx37.1cm \end{gathered}$