Answer: 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
