Question

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 xfeet, 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

Answer 1

Explanation:

The area for a triangle is

`A=(1)/(2)bh`

Our base is given as x, the height is given as 1 more than 6 times the base which looks like this: 6x + 1. We know that the area is 13, so filling in everything:

`13=(1)/(2) (6x+1)(x)`

We can get rid of the denominator of 2 by multiplying it on both sides to get:

`26=(6x+1)(x)` and simplifying a bit:

`26=6x^2+x`

Now we can move over the 26 and put the expression into standard quadratic form by setting it equal to 0:

`6x^2+x-26=0` which is choice C