Question

in the right triangle shown, the length of $overline{ac}=4$ and the length of $overline{ab}=6$. what is the length of $overline{bc}$? choose 1 answer: a $2sqrt{5}$ b $5sqrt{2}$ c $sqrt{2}$ d $sqrt{52}$

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $AB^{2}=AC^{2}+BC^{2}$, so $BC^{2}=AB^{2}-AC^{2}$.

Step2: Substitute given values

Given $AC = 4$ and $AB = 6$, then $BC^{2}=6^{2}-4^{2}=36 - 16=20$.

Step3: Solve for $BC$

$BC=\sqrt{20}=2\sqrt{5}$.

Answer:

A. $2\sqrt{5}$