Answer:
Height: 15 inches.
Base: 24 inches.
Step-by-step explanation:
1. Based on the information shown in the problem, you can write the following expression:
[tex]b=h+9[/tex]
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:
[tex]A=\frac{b*h}{2}\\180=\frac{(h+9)h}{2}\\h^{2}+9h-360=0[/tex]
3. By factoring, you obtain:
[tex](x-15)(x+24)=0\\x_1=15\\x_2=-24[/tex]
4. Choose the positive value. Then, the height is 15 inches.
5. The lenght of the base in inches is:
[tex]b=15+9=24[/tex]
