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

Answer 1

`{5x}^(2) - 2x - 24 = 0`

Explanation:

`area \: a = (base * height)/(2) = (bh)/(2)`

let b = x and h = (5x - 2) then

`a = (x(5x - 2))/(2) = 12 {ft}^(2) \\ a = \frac{ {5x}^(2) - 2x}{2} = 12 {ft }^(2) \\ a = 2 * \frac{ {5x}^(2) - 2x}{2} = 12 {ft}^(2) * 2 \\ a = {5x}^(2) - 2x = 24 {ft}^(2) \\ a = {5x}^(2) - 2x - 24 = 0`

Answer 2

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

Explanation:

The base is x feet.

The height is 2 less that 5 times the base.

The height is 5x - 2.

The area is 12.

The area is base * height / 2.

area = bh/2

area = x * (5x - 2) = 12

5x^2 - 2x = 12

5x^2 - 2x - 12 = 0