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A triangle has sides with lengths of $15\,\text{meters}$ , $16\,\text{meters}$ , and $18\,\text{meters}$ . 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

15\,\text{meters}

,

16\,\text{meters}

, and

18\,\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 right triangle using the Pythagorean theorem. $\newline$ Reasoning: The longest side should be the hypotenuse in a right triangle. $\newline$ Calculation: The sides are $15\,\text{m}$ , $16\,\text{m}$ , and $18\,\text{m}$ . The longest side is $18\,\text{m}$ .
Apply Pythagorean Theorem: Apply the Pythagorean theorem to check if it's a right triangle. $\newline$ Reasoning: For a right triangle, the sum of the squares of the two shorter sides should equal the square of the longest side. $\newline$ Calculation: $15^2 + 16^2 = 225 + 256 = 481$ , $18^2 = 324$ .
Compare Results: Compare the results. $\newline$ Reasoning: If $15^2 + 16^2$ equals $18^2$ , then it's a right triangle. $\newline$ Calculation: $481 \neq 324$ .

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