Question

a triangle has sides with lengths of 77 meters, 81 meters, and 39 meters. is it a right triangle?
yes
no

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 \(a = 39\), \(b = 77\), \(c = 81\) (where \(c\) is the longest side).

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

\(a^2=39^2 = 1521\), \(b^2 = 77^2=5929\), so \(a^2 + b^2=1521 + 5929=7450\).

Step3: Calculate \(c^2\)

\(c^2 = 81^2=6561\).

Step4: Compare \(a^2 + b^2\) and \(c^2\)

Since \(7450
eq6561\), the triangle does not satisfy the Pythagorean theorem.

Answer:

no