Question

apply the pythagorean theorem to decide whether a triangle with side lengths 16 mm, 30 mm, and 32 mm is a right triangle. (1 point)
it is not a right triangle because ( 16 + 30
eq 32 ).
it is a right triangle because ( 16 + 30 = 46 ).
it is not a right triangle because ( 16^{2}+30^{2}
eq 32^{2} ).
it is a right triangle because ( 16^{2}+30^{2}=1,156 ).

Explanation:

Step1: Recall the Pythagorean Theorem

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

Step2: Identify \(a = 16\), \(b = 30\), \(c = 32\)

Calculate \(a^{2}+b^{2}\): \(16^{2}+30^{2}=256 + 900=1156\).
Calculate \(c^{2}\): \(32^{2}=1024\).

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

Since \(1156
eq1024\) (i.e., \(16^{2}+30^{2}
eq32^{2}\)).

Answer:

It is not a right triangle because \(16^{2}+30^{2}
eq32^{2}\).