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?

Answer 1

We must know that the are of the triangle is given by definition by
A = (1/2) * (b) * (h)
where
b = base
h = height
Substituting the values
A = (1/2) * (x) * (1 + 6x)
A = (1/2) * (x + 6x ^ 2)
Since the area is 13 then
(1/2) * (x + 6x ^ 2) = 13
Clearing x we have
6x ^ 2 + x = 26
6x ^ 2 + x-26 = 0
(x-2) * (x + 13/6) = 0
As we look for the base of a triangle then x> 0
x = 2
answer
the base is x = 2
6x ^ 2 + x = 26

Answer 2

`6x^2+x-26 =0`

Explanation:

Given that the area of a triangle has height is 1 more than 6 times its base.

i.e.

base = xfeet gives height

`h=6x+1`

Area of the triangle =
`(1)/(2) bh=(1)/(2)x(6x+1)=13\\6x^2+x=26\\6x^2+x-26 =0\\6x^2-12x+13x-26 =0\\(6x-13)(x+2)=0\\x=-2, x= (13)/(6)`

x cannot be negative as x is length of base.

So solution is
`x=(13)/(6)` and equation is

`6x^2+x-26 =0`