Question

a right triangle has legs with lengths of 11 centimeters and 9 centimeters. what is the length of this triangles hypotenuse, in centimeters?
a $sqrt{40}$
b $sqrt{202}$
c 20
d 202

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with leg lengths \(a\) and \(b\) and hypotenuse length \(c\), \(c^{2}=a^{2}+b^{2}\). Here \(a = 11\) and \(b = 9\).

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

\(a^{2}=11^{2}=121\), \(b^{2}=9^{2}=81\), then \(a^{2}+b^{2}=121 + 81=202\).

Step3: Find the hypotenuse \(c\)

Since \(c^{2}=202\), then \(c=\sqrt{202}\).

Answer:

B. \(\sqrt{202}\)