Question

square roots and right triangles
which equation could be used to find the length of the hypotenuse?
$11^{2}-6^{2}=c^{2}$
$c^{2}-6^{2}=11^{2}$
$6^{2}+11^{2}=c^{2}$
$6^{2}+c^{2}=11^{2}$

Explanation:

Step1: Recall the Pythagorean theorem

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

Step2: Identify the legs and hypotenuse

In \(\triangle ABC\), \(AC = 6\mathrm{cm}\) and \(BC=11\mathrm{cm}\) are the legs, and \(AB = c\) is the hypotenuse.

Step3: Substitute into the Pythagorean theorem

Substitute \(a = 6\) and \(b = 11\) into \(a^{2}+b^{2}=c^{2}\), we get \(6^{2}+11^{2}=c^{2}\).

Answer:

\(6^{2}+11^{2}=c^{2}\)