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A triangle has sides with lengths of $4\,\text{miles}$ , $6\,\text{miles}$ , and $8\,\text{miles}$ . 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

4\,\text{miles}

,

6\,\text{miles}

, and

8\,\text{miles}

. 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 $4$ , $6$ , and $8$ . The longest side is $8$ .
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: $4^2 + 6^2 = 16 + 36 = 52$ , $8^2 = 64$
Compare Results: Compare the results to determine if it's a right triangle. $\newline$ Reasoning: If the sum of the squares of the two shorter sides equals the square of the longest side, it's a right triangle. $\newline$ Calculation: $52 \neq 64$

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