# What is the perimeter and area of a triangle that measures 5, 5, and 5 square root 2?

Apr 20, 2016

Perimeter: $10 + 5 \sqrt{2}$
Area: $12 \frac{1}{2}$ sq.units

#### Explanation:

The dimensions given are those of a standard right-angled triangle with two ${45}^{\circ}$ angles.

The perimeter is simply the sum of the lengths of the given sides.

Since this is a right-angled triangle, we can use the non-hypotenuse sides as a base($b$) and height($h$).

${\text{Area}}_{\triangle} = \frac{1}{2} b h = \frac{1}{2} \cdot 5 \cdot 5 = \frac{25}{2} = 12 \frac{1}{2}$