Question

(pythagorean theorem mc)
the shortest side of a right triangle measures 9, and the longest side measures 15. determine the measurement of the unknown side.
8
11
12
15

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (longest side). Let \(a = 9\), \(c=15\), and \(b\) be the unknown side. Then \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute values

\(b^{2}=15^{2}-9^{2}\). Since \(15^{2}=225\) and \(9^{2}=81\), we have \(b^{2}=225 - 81\).

Step3: Calculate \(b^{2}\)

\(b^{2}=144\).

Step4: Find \(b\)

Take the square root of both sides. \(b=\sqrt{144}\), and \(b = 12\).

Answer:

12