Question

The area of a triangle is 24 square inches. What is the height of the triangle if the base length is 4 inches?

6 inches
8 inches
12 inches
20 inches

Answer 1

`\boxed {\boxed { \sf 12 \ inches}}`

Explanation:

The area of a triangle can be calculated using the following formula.

`a=(1)/(2) bh`

The area of the triangle is 24 square inches and the base is 4 inches long.

• a= 24 in²
• b= 4 in

Substitute the values into the formula.

`24 \ in^2 = \frac {1}{2} * 4 \ in * h`

Multiply on the right side of the equation.

`24 \ in ^2 = ( (1)/(2) * 4 \ in ) * h`

`24 \ in ^2 =2 \ in *h`

We are solving for the height of the triangle, so we must isolate the variable h. It is being multiplied by 2 inches. The inverse of multiplication is division, so we divide both sides by 2 inches.

`\frac { 24 \ in ^2 }{2 \ in }= ( 2 \ in *h)/( 2 \ in)`

`\frac { 24 \ in ^2 }{2 \ in }= h`

`12 \ in = h`

The height of the triangle is 12 inches.