Question

if a triangle has sides measuring 60, 75, and 45, is it a right triangle? (1 point)
no, because 9,225 does not equal 2,025.
yes, because 3,600 equals 3,600.
yes, because 5,625 equals 5,625.
no, because 5,625 does not equal 3,600.

Explanation:

Step1: Recall the Pythagorean theorem

For a right - triangle with sides \(a\), \(b\), \(c\) (\(c\) is the longest side), \(a^{2}+b^{2}=c^{2}\). Here \(a = 45\), \(b=60\), \(c = 75\).

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

• Calculate \(a^{2}+b^{2}\):

\(a^{2}=45^{2}=2025\), \(b^{2}=60^{2}=3600\), then \(a^{2}+b^{2}=2025 + 3600=5625\).

• Calculate \(c^{2}\):

\(c^{2}=75^{2}=5625\).

Answer:

Yes, because \(5,625\) equals \(5,625\).