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

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above