Question

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

Explanation:

Step1: Identify the hypotenuse

The hypotenuse is the longest side of a right - triangle. Here, the hypotenuse $c = 25$ and one side $a = 24$.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$, where $c$ is the hypotenuse and $a$ and $b$ are the other two sides. We want to find $b$, so we can rewrite the formula as $b=\sqrt{c^{2}-a^{2}}$.
Substitute $c = 25$ and $a = 24$ into the formula: $b=\sqrt{25^{2}-24^{2}}=\sqrt{(25 + 24)(25 - 24)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$).

Step3: Calculate the value of $b$

First, $(25 + 24)(25 - 24)=(49)\times(1)=49$. Then $\sqrt{49}=7$.

Answer:

7