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.
o 2.4 inches
o 3.2 inches
o 10.0 inches
o 15.7 inches

Explanation:

Step1: Consider the third - side as hypotenuse

Use the Pythagorean theorem $c=\sqrt{a^{2}+b^{2}}$. Here $a = 5$ and $b = 8$, so $c=\sqrt{5^{2}+8^{2}}=\sqrt{25 + 64}=\sqrt{89}\approx9.4$.

Step2: Consider one of the given sides as hypotenuse

Assume 8 is the hypotenuse, and find the other leg using $b=\sqrt{c^{2}-a^{2}}$. So $b=\sqrt{8^{2}-5^{2}}=\sqrt{64 - 25}=\sqrt{39}\approx6.2$.

Step3: Calculate the difference

Find the difference between the two possible lengths of the third - side: $9.4−6.2 = 3.2$.

Answer:

3.2 inches