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 unknown leg be $x$. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a,b$ are the legs. Here, $c = 20$, $a=12$, and $b = x$. So $x^{2}=c^{2}-a^{2}$.

Step2: Substitute values

$x^{2}=20^{2}-12^{2}=400 - 144=256$.

Step3: Solve for $x$

$x=\sqrt{256}=16$.

Answer:

C. 16 units