Question

in the right triangle shown below, what is the length of the missing side length labeled n? 24 7 n 25 29 \sqrt{503} \sqrt{711}

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 7\), \(b=24\) and hypotenuse \(n\), the Pythagorean theorem is \(a^{2}+b^{2}=n^{2}\).
So, \(n^{2}=7^{2}+24^{2}\).

Step2: Calculate \(7^{2}+24^{2}\)

\(7^{2}=49\) and \(24^{2}=576\). Then \(n^{2}=49 + 576\).
\(n^{2}=625\).

Step3: Solve for \(n\)

Take the square root of both sides: \(n=\sqrt{625}\). Since \(n>0\) (length of a side), \(n = 25\).

Answer:

25