Question

a triangle has sides with lengths of 11 centimeters, 34 centimeters, and 40 centimeters. is it a right triangle?

Explanation:

Step1: Recall the Pythagorean theorem

For a right - triangle with side lengths \(a\), \(b\), and \(c\) (\(c\) is the longest side), \(a^{2}+b^{2}=c^{2}\). Here, \(a = 11\), \(b=34\), \(c = 40\).

Step2: Calculate \(a^{2}+b^{2}\) and \(c^{2}\)

• Calculate \(a^{2}+b^{2}\): \(11^{2}+34^{2}=121 + 1156=1277\).
• Calculate \(c^{2}\): \(40^{2}=1600\).

Since \(11^{2}+34^{2}
eq40^{2}\), it is not a right - triangle.

Answer:

no