Question

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

Explanation:

Step1: Apply Pythagorean theorem

Let the hypotenuse $c = 25$ and one - side $a = 24$. The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$, so $b^{2}=c^{2}-a^{2}$.

Step2: Substitute values

Substitute $c = 25$ and $a = 24$ into the formula $b^{2}=c^{2}-a^{2}$. We get $b^{2}=25^{2}-24^{2}=(25 + 24)(25 - 24)$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). Then $b^{2}=(49)\times(1)=49$.

Step3: Solve for $b$

Take the square root of both sides. Since $b>0$ (as it represents the length of a side of a triangle), $b=\sqrt{49}=7$.

Answer:

7