# What is the perimeter and area of a right triangle with a hypotenuse of 26 and a leg of 24?

May 23, 2018

$\text{Perimeter} = 60$ and $\text{Area} = 120$

#### Explanation:

Assign the sides $b = 24 \mathmr{and} c = 26$

Use the Pythagorean theorem,

${c}^{2} = {a}^{2} + {b}^{2}$

,to find the length of side a:

$a = \sqrt{{26}^{2} - {24}^{2}}$

$a = 10$

The perimeter is:

$\text{Perimeter} = a + b + c$

$\text{Perimeter} = 10 + 24 + 26$

$\text{Perimeter} = 60$

The area is:

$\text{Area} = \frac{1}{2} b h$

If we select side b as the base, then side a is the height:

$\text{Area} = \frac{1}{2} \left(24\right) \left(10\right)$

$\text{Area} = 120$