Question

the area of a right triangle is 336 square centimeters. the base of the right triangle is 48 centimeters. what is the length of the hypotenuse of the right triangle? enter your answer in the box. \boxed{} cm

Explanation:

Step1: Find the height of the triangle

The area formula for a right triangle is $A = \frac{1}{2} \times base \times height$. We know $A = 336$ and $base = 48$. So we solve for $height$:
$336=\frac{1}{2}\times48\times height$
$336 = 24\times height$
$height=\frac{336}{24}=14$

Step2: Use Pythagorean theorem to find hypotenuse

The Pythagorean theorem is $c=\sqrt{a^{2}+b^{2}}$, where $a = 48$, $b = 14$.
First, calculate $a^{2}+b^{2}$:
$48^{2}+14^{2}=2304 + 196=2500$
Then take the square root:
$c=\sqrt{2500}=50$

Answer:

50