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A triangle has sides with lengths of $9\,\text{meters}$ , $12\,\text{meters}$ , and $15\,\text{meters}$ . 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

9\,\text{meters}

,

12\,\text{meters}

, and

15\,\text{meters}

. Is it a right triangle?

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Identify longest side: Identify the longest side to test for the hypotenuse. $\newline$ Given sides: $9\,\text{m}$ , $12\,\text{m}$ , $15\,\text{m}$ . $\newline$ Longest side (potential hypotenuse): $15\,\text{m}$ .
Apply Pythagorean Theorem: Apply the Pythagorean Theorem to check if it's a right triangle. $\newline$ Using the formula: $a^2 + b^2 = c^2$ , where $c$ is the hypotenuse. $\newline$ Calculate: $9^2 + 12^2 = 81 + 144 = 225$ .
Compare sum of squares: Compare the sum of squares of the other two sides to the square of the longest side. $\newline$ Check: $225$ (sum from Step $2$ ) $= 15^2 = 225$ .

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