Question

1. find the perimeter and area of this triangle. dimensions are in inches.

(image of a right triangle with legs 5 inches and 12 inches, hypotenuse 13 inches)

Explanation:

Step1: Calculate the perimeter

The perimeter of a triangle is the sum of its three sides. The sides are 5 inches, 12 inches, and 13 inches.
$Perimeter = 5 + 12 + 13$
$Perimeter = 30$ inches.

Step2: Calculate the area

This is a right - triangle (since $5^{2}+12^{2}=25 + 144 = 169=13^{2}$, by Pythagorean theorem). The area of a right - triangle is given by the formula $A=\frac{1}{2}\times base\times height$. We can take the base as 12 inches and the height as 5 inches.
$Area=\frac{1}{2}\times12\times5$
$Area = 30$ square inches.

Answer:

Perimeter: 30 inches, Area: 30 square inches