Question

a triangle has sides with lengths of 72 millimeters, 96 millimeters, and 57 millimeters. 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 \(a = 57\), \(b = 72\), \(c = 96\) (where \(c\) is the longest side).

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

\(a^2 = 57^2 = 3249\), \(b^2 = 72^2 = 5184\), so \(a^2 + b^2 = 3249 + 5184 = 8433\).

Step3: Calculate \(c^2\)

\(c^2 = 96^2 = 9216\).

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

Since \(8433
eq 9216\), the triangle does not satisfy the Pythagorean theorem.

Answer:

no