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:
[tex]7.5^2=4.5^2+6^2[/tex]
By the theorem. Then:
[tex]\begin{gathered} 7.5^2=56.25 \\ 4.5^2+6^2=20.25+36=56.25 \end{gathered}[/tex]
They're equal, then the lengths correspond to a right triangle.
For part 2, we need to use again the theorem. In this case:
[tex]\begin{gathered} 12^2+x^2=39^2 \\ x=\sqrt{1521-144} \\ x=\sqrt{1377} \\ x\approx37.1cm \end{gathered}[/tex]
