Question

1. a right triangle has leg lengths of 12 centimeters and 16 centimeters. what is the length of the hypotenuse?

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle with legs $a, b$ and hypotenuse $c$, $c^2 = a^2 + b^2$

Step2: Substitute given leg lengths

Let $a=12$, $b=16$. Calculate $a^2 + b^2$:
$12^2 + 16^2 = 144 + 256 = 400$

Step3: Solve for hypotenuse $c$

Take square root of 400:
$c = \sqrt{400} = 20$

Answer:

20 centimeters