Question

does ( a^{2}+b^{2}=c^{2} ) hold true for this right triangle?
( a = 7 )
( b = 5 )
( c=sqrt{74} )
( a^{2}+b^{2}stackrel{?}{=}c^{2} )

no, ( a^{2}+b^{2}=c^{2} ) is not true for this right triangle. yes, ( a^{2}+b^{2}=c^{2} ) is true for this right triangle.

Explanation:

Step1: Calculate \(a^{2}+b^{2}\)

\(a = 7\), \(b = 5\), so \(a^{2}+b^{2}=7^{2}+5^{2}=49 + 25=74\)

Step2: Calculate \(c^{2}\)

\(c=\sqrt{74}\), so \(c^{2}=(\sqrt{74})^{2}=74\)

Step3: Compare \(a^{2}+b^{2}\) and \(c^{2}\)

Since \(a^{2}+b^{2}=74\) and \(c^{2}=74\), then \(a^{2}+b^{2}=c^{2}\)

Answer:

Yes, \(a^{2}+b^{2}=c^{2}\) is true for this right triangle.