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

Answer:

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

Step-by-step 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 = $\frac{1}{2} bh=\frac{1}{2}x(6x+1)=13\\6x^2+x=26\\6x^2+x-26 =0\\6x^2-12x+13x-26 =0\\(6x-13)(x+2)=0\\x=-2, x= \frac{13}{6}$

x cannot be negative as x is length of base.

So solution is $x=\frac{13}{6}$ and equation is

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

Answer 2

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