Question

in the right triangle shown, the length of $overline{ac}=4$ and the length of $overline{ab}=10$. what is the length of $overline{bc}$? choose 1 answer: a 84 b $2sqrt{21}$ c $21sqrt{2}$ d $sqrt{116}$

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(AB^{2}=AC^{2}+BC^{2}\), where \(AB\) is the hypotenuse. We know \(AB = 10\) and \(AC = 4\), and we need to find \(BC\). Rearranging the formula for \(BC\), we get \(BC=\sqrt{AB^{2}-AC^{2}}\).

Step2: Substitute values

Substitute \(AB = 10\) and \(AC = 4\) into the formula: \(BC=\sqrt{10^{2}-4^{2}}=\sqrt{100 - 16}=\sqrt{84}=2\sqrt{21}\).

Answer:

B. \(2\sqrt{21}\)