Question

the lengths of two sides of a right triangle are 5 inches and 8 inches. what is the difference between the two possible lengths of the third side of the triangle? round your answer to the nearest tenth. 2.4 inches 3.2 inches 10.0 inches 15.7 inches

Explanation:

Step1: Consider two cases using Pythagorean theorem

Case 1: Third - side is hypotenuse. Let \(a = 5\) and \(b = 8\). By \(c=\sqrt{a^{2}+b^{2}}\), we have \(c=\sqrt{5^{2}+8^{2}}=\sqrt{25 + 64}=\sqrt{89}\approx9.4\). Case 2: Third - side is a leg. Let \(a = 5\) and \(c = 8\). By \(b=\sqrt{c^{2}-a^{2}}\), we have \(b=\sqrt{8^{2}-5^{2}}=\sqrt{64 - 25}=\sqrt{39}\approx6.2\).

Step2: Calculate the difference

The difference between the two possible lengths is \(9.4−6.2 = 3.2\).

Answer:

3.2 inches