Question

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. 5x2 − 2x − 24 = 0
B. 5x2 − 2x − 6 = 0
C. 5x2 − 2x − 12 = 0
D. 25x2 − 10x − 24 = 0

Answer 1

C. 5x^2 − 2x − 24 = 0

Explanation:

Answer 2

A. 5x^2 − 2x − 24 = 0

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