Question

one of the legs of a right triangle measures 12 cm and the other leg measures 9 cm. find the measure of the hypotenuse. if necessary, round to the nearest tenth.

Explanation:

Step1: Recall Pythagorean theorem

The Pythagorean theorem for a right - triangle is \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the legs and \(c\) is the hypotenuse.

Step2: Substitute the values of the legs

Let \(a = 12\) cm and \(b=9\) cm. Then \(c^{2}=12^{2}+9^{2}\). Calculate \(12^{2}=144\) and \(9^{2}=81\). So \(c^{2}=144 + 81=225\).

Step3: Solve for \(c\)

Take the square root of both sides. \(c=\sqrt{225}=15\) cm.

Answer:

15 cm