Question

r
36
45
s
27
t

Explanation:

Step1: Check the Pythagorean theorem

For a right - triangle, the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs of the right - triangle.
Let \(a = 27\), \(b = 36\), and \(c = 45\).
Calculate \(a^{2}+b^{2}\):
\(a^{2}+b^{2}=27^{2}+36^{2}\)
\(=729 + 1296\)
\(=2025\)
Calculate \(c^{2}\):
\(c^{2}=45^{2}=2025\)

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

Since \(a^{2}+b^{2}=2025\) and \(c^{2}=2025\), we have \(a^{2}+b^{2}=c^{2}\)

Answer:

The triangle is a right - triangle as it satisfies the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) (where \(a = 27\), \(b = 36\), \(c = 45\))