Question

the lengths of the legs of a right triangle are 5 centimeters and 10 centimeters. which of the following measures is closest to the length of the hypotenuse? 11.2 cm 11.4 cm 11.6 cm 11.8 cm

Explanation:

Step1: Apply Pythagorean theorem

Let \(a = 5\) and \(b=10\). The Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\), so \(c=\sqrt{a^{2}+b^{2}}\).

Step2: Substitute values

\(c=\sqrt{5^{2}+ 10^{2}}=\sqrt{25 + 100}=\sqrt{125}\).

Step3: Calculate square - root

\(\sqrt{125}\approx11.18\).

Answer:

11.2 cm