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. 25x^2-10x-24=0

B. 5x^2-2x-24=0

C. 5x^2-2x-6=0

D. 5x^2-2x-12=0

A. 5x^2 - 2x - 24 = 0

Step-by-step explanation:

height = 5b-2

b = x

We can rewrite the height as

h = 5x-2

We know the formula for area of a triangle

A = 1/2 bh

A = 1/2 x * (5x-2)

Distributing the x

A = 1/2 (5x^2 - 2x)

We know A = 12

12 = 1/2 (5x^2 - 2x)

Multiply each side by 2

12*2 = 2*1/2 (5x^2 - 2x)

24 = 5x^2 - 2x

Subtract 24 from each side

24-24 = 5x^2 - 2x-24

0 = 5x^2 - 2x-24