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A triangle has sides with lengths of $11\,\text{meters}$ , $14\,\text{meters}$ , 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

11\,\text{meters}

,

14\,\text{meters}

, and

15\,\text{meters}

. Is it a right triangle?

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Identify longest side: Step $1$ : Identify the longest side to test for the hypotenuse. $\newline$ Given side lengths: $11\,\text{m}$ , $14\,\text{m}$ , $15\,\text{m}$ . $\newline$ The longest side is $15\,\text{m}$ , which could be the hypotenuse if this is a right triangle.
Apply Pythagorean Theorem: Step $2$ : 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 $11^2 + 14^2$ and compare it to $15^2$ . $\newline$ $11^2 = 121$ , $14^2 = 196$ , $15^2 = 225$ . $\newline$ $121 + 196 = 317$ .
Compare side lengths: Step $3$ : Compare the sum of squares of the shorter sides to the square of the longest side. $\newline$ Since $317 \neq 225$ , the sides do not satisfy the Pythagorean Theorem. $\newline$ Therefore, the triangle is not a right triangle.

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