Question

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

Explanation:

Step1: Identify the theorem

Use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse of a right - triangle. Here, assume the hypotenuse $c = 26$ and one side $a = 24$.

Step2: Rearrange the formula

We want to find the other side $b$. Rearranging the Pythagorean theorem gives $b=\sqrt{c^{2}-a^{2}}$.

Step3: Substitute 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 $b=\sqrt{50\times2}=\sqrt{100}$.

Step4: Calculate the result

$\sqrt{100}=10$.

Answer:

10