Question

side a on a right triangle is always the longest side. false true

Explanation:

Step1: Recall the Pythagorean theorem

In a right - triangle, \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs.

Step2: Analyze the relationship between sides

Since \(c^{2}=a^{2}+b^{2}\), then \(c=\sqrt{a^{2}+b^{2}}\). For non - zero positive values of \(a\) and \(b\) (\(a>0,b > 0\)), \(\sqrt{a^{2}+b^{2}}>\sqrt{a^{2}}=a\) and \(\sqrt{a^{2}+b^{2}}>\sqrt{b^{2}}=b\). So the hypotenuse (side \(c\)) is always the longest side in a right - triangle.

Answer:

false