Question

a triangle has sides with lengths of 12 centimeters, 35 centimeters, and 37 centimeters. is it a right triangle? yes no

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\) where \(c\) is the longest side. Here, \(a = 12\), \(b = 35\), \(c = 37\).

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

\(12^2 + 35^2 = 144 + 1225 = 1369\)

Step3: Calculate \(c^2\)

\(37^2 = 1369\)

Step4: Compare results

Since \(12^2 + 35^2 = 37^2\), the triangle satisfies the Pythagorean theorem.

Answer:

yes