Question

the hypotenuse of a right triangle is 20 units long. one leg of the triangle is 12 units long as shown in the figure. what is the length of the other leg? a. 16.8 units b. 20 units c. 16 units d. 23 units

Explanation:

Step1: Apply Pythagorean theorem

Let the length of the other leg be $x$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 20$ (hypotenuse) and $a = 12$ (one leg), so $x=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

$x=\sqrt{20^{2}-12^{2}}=\sqrt{(20 + 12)(20 - 12)}$ (using the difference - of - squares formula $a^{2}-b^{2}=(a + b)(a - b)$).
$=\sqrt{32\times8}=\sqrt{256}$.

Step3: Calculate the square - root

$\sqrt{256}=16$.

Answer:

C. 16 units