Question

is a triangle with side lengths 106, 56, and 90 a right triangle? no yes

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, the sum of the squares of the two shorter sides should equal the square of the longest side. Let \( a = 56 \), \( b = 90 \), \( c = 106 \) (longest side).

Step2: Calculate \( a^2 + b^2 \)

\( a^2 = 56^2 = 3136 \), \( b^2 = 90^2 = 8100 \), so \( a^2 + b^2 = 3136 + 8100 = 11236 \).

Step3: Calculate \( c^2 \)

\( c^2 = 106^2 = 11236 \).

Step4: Compare results

Since \( a^2 + b^2 = c^2 \) (11236 = 11236), the triangle satisfies the Pythagorean theorem.

Answer:

yes