Question

Given that triangle, LMN has side lengths of 18.5 inches, 10 inches, and 15.5 inches, prove triangle LMN is a right triangle.Explain by applying the Converse of the Pythagorean Theorem. Drag numbers to order the proof.1 2 3 4 5340 ≠ 342.25 =?102 + 15.52 =? 18.52 =?a2 + b2 =? 18.52 =?100 + 240.25 =? 342.5 =?Therefore, triangle LMN is not a right triangle. =?

Answer 1

Given:

The triangle, LMN has side lengths of 18.5 inches, 10 inches, and 15.5 inches

Using the converse of the Pythagorean theorem

So,

$\begin{gathered} 18.5^2=342.25 \\ 10^2=100 \\ 15.5^2=240.25 \\ 10^2+15.5^2=340.2\ne342.25 \end{gathered}$

So, the triangle LMN is not a right-angle triangle

The order of proof is as follows:

$\begin{gathered} 1)10^2+15.5^2=340.2 \\ 2)a^2+b^2=340.2 \\ 3)18.5^2=342.25 \\ 4)340.25\ne342.25 \\ 5)\text{LMN not right triangle} \end{gathered}$