Question

a triangle has sides that measure 5 units, 7 units, and 8 units. is this triangle a right triangle?
o yes, it is a right triangle because ( 5 ^ { 2 } + 7 ^ { 2 } = 8 ^ { 2 } )
o no, it is not a right triangle because ( 5 ^ { 2 } + 7 ^ { 2 } = 8 ^ { 2 } )
o no, it is not a right triangle because ( 5 ^ { 2 } + 7 ^ { 2 }
eq 8 ^ { 2 } )
o yes, it is a right triangle because ( 5 ^ { 2 } + 7 ^ { 2 } = 8 ^ { 2 } )

Explanation:

Step1: Recall the Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side. Here \(a = 5\), \(b=7\), \(c = 8\).

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

\(a^{2}+b^{2}=5^{2}+7^{2}=25 + 49=74\)
\(c^{2}=8^{2}=64\)
Since \(a^{2}+b^{2}
eq c^{2}\) (i.e., \(74
eq64\)), the triangle is not a right - triangle.

Answer:

No, it is not a right triangle because \(5^{2}+7^{2}
eq8^{2}\)