Question

An isosceles triangle has a perimeter of 32 inches and a base 12 inches long. Determine the height and area of the triangle:

Hint: Use the formula sheet to determine the formula(s) needed to solve the problem.
Height
in.
Area =
in.

Answer 1

Explanation:

We can start by using the perimeter of the triangle to find the length of the other two sides. Since the triangle is isosceles, the other two sides must be equal. Let's call the length of each of these sides "x". Then we have:

Perimeter = 32 = 12 + x + x

Simplifying this equation, we get:

32 = 12 + 2x

20 = 2x

x = 10

So the length of each of the other two sides is 10 inches.

To find the height of the triangle, we can use the Pythagorean Theorem. Let's call the height "h". Then we have:

h^2 = 10^2 - (12/2)^2

h^2 = 100 - 36

h^2 = 64

h = 8

So the height of the triangle is 8 inches.

Finally, we can use the formula for the area of a triangle to find the area of the triangle. Let's call the area "A". Then we have:

A = (1/2)bh

A = (1/2)(12)(8)

A = 48

So the area of the triangle is 48 square inches.

Therefore, the height of the triangle is 8 inches and the area of the triangle is 48 square inches.