Question

find the length of the third side. if necessary, round to the nearest tenth. answer attempt 1 out of 2 submit answer

Explanation:

Step1: Identify the theorem

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here \(c = 25\) and one - leg \(a = 7\), and we want to find the other leg \(b\).

Step2: Rearrange the formula

We get \(b=\sqrt{c^{2}-a^{2}}\).

Step3: Substitute values

Substitute \(c = 25\) and \(a = 7\) into the formula: \(b=\sqrt{25^{2}-7^{2}}=\sqrt{(25 + 7)(25 - 7)}\) (using \(x^{2}-y^{2}=(x + y)(x - y)\)). First, \(25+7 = 32\) and \(25 - 7=18\), so \(b=\sqrt{32\times18}=\sqrt{576}\).

Step4: Calculate the square - root

\(\sqrt{576}=24\).

Answer:

24