Question

the legs of a right triangle measure 5 centimeters and 12 centimeters. what is the length of the hypotenuse? a. 17 centimeters b. 14 centimeters c. 169 centimeters d. 13 centimeters

Explanation:

Step1: Apply Pythagorean theorem

Let \(a = 5\) and \(b=12\). The Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\), so \(c^{2}=5^{2}+12^{2}\).

Step2: Calculate squares

\(5^{2}=25\) and \(12^{2} = 144\), then \(c^{2}=25 + 144=169\).

Step3: Find the square - root

\(c=\sqrt{169}=13\) (we take the positive square - root since length cannot be negative).

Answer:

D. 13 centimeters