Question

The base of a triangle exceeds the height by 9 inches. If the area is 180 square inches, find the length of the base and the height of the triangle.

Answer 1

Height: 15 inches.

Base: 24 inches.

Explanation:

1. Based on the information shown in the problem, you can write the following expression:

`b=h+9`

Where b is the base and h is the height.

2. Substitute the expression into the formula fo calculate the area of a triangle and solve for h:

`A=(b*h)/(2)\\180=((h+9)h)/(2)\\h^(2)+9h-360=0`

3. By factoring, you obtain:

`(x-15)(x+24)=0\\x_1=15\\x_2=-24`

4. Choose the positive value. Then, the height is 15 inches.

5. The lenght of the base in inches is:

`b=15+9=24`