Question

triangles
which equation could be used to find the length of the hypotenuse?
$5^{2}-2^{2}=c^{2}$
$2^{2}+c^{2}=5^{2}$
$2^{2}+5^{2}=c^{2}$
$c^{2}-2^{2}=5^{2}$

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\).

Step2: Identify legs and hypotenuse

In \(\triangle ABC\), \(a = 2\) (one leg), \(b = 5\) (another leg), and \(c\) is the hypotenuse.

Step3: Substitute values into Pythagorean theorem

Substitute \(a = 2\) and \(b = 5\) into \(a^{2}+b^{2}=c^{2}\), we get \(2^{2}+5^{2}=c^{2}\).

Answer:

\(2^{2}+5^{2}=c^{2}\)