Question

Use a geometric formula to solve the problem. A triangle has a height of 8 feet and an area of 48 square feet. Find the base.

Answer 1

The formula for finding area of a triangle is:

`(1)/(2)bh`

The base is 8 feet. The area is 48 ft². Put that into the formula:

`(1)/(2) b8 = 48`

Remember that you have to multiply the base × height by
`(1)/(2)`, which is the same as dividing by 2. To find the height, you need to multiply the area by 2, instead of dividing.

`Area = 48 sq\ ft^(2) \\ 48 * 2 = 96`

That means the base × height is equal to 96. You already know the height. To find the base, divide the (base × height) by the height. The height is 8.

`96 / 8 = 12`

That means the base of the triangle is 12 ft

CHECK

`(1)/(2)bh`

Base = 12

Height = 8

Put that into the formula:

`12 \cdot 8 \cdot (1)/(2) = 96 \cdot (1)/(2) = 96 / 2 = 48` ✔

BASE = 12 ft