Question

what side(s) will always be the longest on a right triangle?
leg a
the hypotenuse
leg b
the right angle

Explanation:

Step1: Recall Pythagorean theorem

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

Step2: Analyze the relationship of side lengths

Since \(a^{2}+b^{2}=c^{2}\), 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 \(\sqrt{a^{2}+b^{2}}>\sqrt{b^{2}}=b\).

Answer:

The hypotenuse.