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?

1) 6x^2+x-12=0
2) 6x^2+x-13=0
3) 6x^2+x-26=0
4) 36x^2+6x-26=0

Question

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?

1) 6x^2+x-12=0
2) 6x^2+x-13=0
3) 6x^2+x-26=0
4) 36x^2+6x-26=0

displayerror · Answer

The area of a triangle is given by $$\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}$$
We need to develop expressions for the $\text{Base}$ and $\text{Height}$ terms.

We know what the base is--we're told that it can be represented by $\text{Base} = x$
We're also told that the height is "1 more than 6 times its base". Let's break this down into math.
"1 more than" suggests addition. Think about this: wouldn't you say that 3 apples is 1 more than 2 apples?
"6 times its base" suggests multiplication. After all, that's the expression we typically use to express multiplication.

You should be able to create an expression for the $\text{Height}$ term now. Plug all of your information into the expression for $\text{Area}$ and simplify to get an expression similar to the choices provided.