Question

1. an engineer is designing a support structure in the shape of a right triangle. the base is 12 meters, and the height is 16 meters. what is the length of the diagonal support? a. 20 meters b. 24 meters c. 18 meters d. 15 meters

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, the Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $a$ and $b$ are the legs of the right - triangle and $c$ is the hypotenuse. Here, $a = 12$ and $b = 16$.
So, $12^{2}+16^{2}=c^{2}$.
$12^{2}=144$ and $16^{2}=256$.
Then $144 + 256=c^{2}$, and $c^{2}=400$.

Step2: Solve for $c$

Take the square root of both sides. Since $c>0$ (as it represents a length), $c=\sqrt{400}=20$.

Answer:

a. 20 meters