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A triangle has sides with lengths of $6\,\text{yards}$ , $8\,\text{yards}$ , and $10\,\text{yards}$ . Is it a right triangle? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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Converse of the Pythagorean theorem: is it a right triangle?

Full solution

Q. A triangle has sides with lengths of

6\,\text{yards}

,

8\,\text{yards}

, and

10\,\text{yards}

. Is it a right triangle?

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Identify longest side: Identify the longest side to test for the right triangle using the Pythagorean theorem.
Apply Pythagorean theorem: Apply the Pythagorean theorem: $a^2 + b^2 = c^2$ , where $c$ is the hypotenuse (longest side) and $a$ , $b$ are the other two sides.
Check sum of squares: Check if the sum of the squares of the two shorter sides equals the square of the longest side.

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