Select the correct answer. The area of a triangle whose height is 1 more than 6 times its base is 13 square feet. If the base of the triangle is x feet, which equation models this situation? A. 6x2 + x − 12 = 0 B. 6x2 + x − 13 = 0 C. 6x2 + x − 26 = 0 D. 36x2 + 6x − 26 = 0

The correct answer is C: 6x² + x - 26 = 0

Step-by-step explanation: All the variables in the question have been identified, that is, the area, the height and the base of the triangle. The area of a triangle is defined as

Area = ½ x B x H

Area = 13,

Base = B and

Height = 6B + 1

The question states that the height is 1 more than 6 times it's base. Hence the height would be, Base x 6, plus 1, that is, 6B + 1

The area can now be expressed properly as follows,

13 = ½ x B x (6B + 1)

By cross multiplication we now have

2 x 13 = B (6B + 1)

26 = 6B² + B

Subtract 26 from both sides of the equation

6B² + B - 26 = 0

However, the answer uses x as the unknown variable. So if you use x as the base of the triangle instead of B, your answer would result in

6x² + x - 26 = 0