Question

find the length of the third side. if necessary, round to the nearest tenth.

Explanation:

Step1: Identify the theorem

Since it's a right - triangle, use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (the longest side). Here, assume the hypotenuse \(c = 26\) and one side \(a = 24\), and we want to find the other side \(b\).

Step2: Rearrange the formula

We can rewrite the Pythagorean theorem as \(b=\sqrt{c^{2}-a^{2}}\).

Step3: Substitute the values

Substitute \(c = 26\) and \(a = 24\) into the formula: \(b=\sqrt{26^{2}-24^{2}}=\sqrt{(26 + 24)(26 - 24)}\) (using the difference - of - squares formula \(x^{2}-y^{2}=(x + y)(x - y)\)). Then \(b=\sqrt{50\times2}=\sqrt{100}=10\).

Answer:

10