Question

a triangle with sides of lengths 32, 60, and 68 is a right triangle. a. true b. false

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side.

Step2: Identify the sides

Let \(a = 32\), \(b = 60\), and \(c = 68\).

Step3: Calculate \(a^{2}+b^{2}\)

\(a^{2}=32^{2}=32\times32 = 1024\), \(b^{2}=60^{2}=60\times60 = 3600\). Then \(a^{2}+b^{2}=1024 + 3600=4624\).

Step4: Calculate \(c^{2}\)

\(c^{2}=68^{2}=68\times68 = 4624\).

Step5: Compare

Since \(a^{2}+b^{2}=c^{2}\), the triangle is a right - triangle.

Answer:

A. True