Question

select the correct answer. the height of a triangle is 2 less than 5 times its base. if the base of the triangle is x feet, and the area of the triangle is 12 square feet, which equation models this situation?

a. (5x^{2}-2x - 6=0)
b. (25x^{2}-10x - 24 = 0)
c. (5x^{2}-2x - 12=0)
d. (5x^{2}-2x - 24=0)

Explanation:

Step1: Express the height in terms of base

Given base is $x$ feet. Height is 2 less than 5 times the base, so height $h = 5x - 2$.

Step2: Use the area formula for a triangle

The area formula for a triangle is $A=\frac{1}{2}bh$. We know $A = 12$, $b=x$ and $h = 5x - 2$. Substitute these values: $12=\frac{1}{2}x(5x - 2)$.

Step3: Simplify the equation

Multiply both sides by 2 to get rid of the fraction: $24=x(5x - 2)$. Expand the right - hand side: $24 = 5x^{2}-2x$. Rearrange to standard quadratic form: $5x^{2}-2x - 24=0$.

Answer:

D. $5x^{2}-2x - 24 = 0$