Formula of Area of triangle.... A=1/2bh where A is area, b is the base, and h is height.
h= 3b-1
Area=12
At this point you want to plug in what you know into the equation.
12=1/2b(3b-1)
Then you can solve for b. First multiply each side by 2 to cancel the fraction.
24=b(3b-1)
Then distribute the b term.
24=3b^2 - b
Then set the equation equal to zero.
0=3b^2-b-24
Then either factor or use the quadratic equation to solve for b.
0=(3b-8)(b-3)
which means that b=3 and b=8/3
You then plug both answers back into the original equation (12=1/2b(3b-1))and see if there are any extraneous solutions. When you do, you can see that 8/3 as an answer does not equal 12. Therefore, the correct answer and the base of the triangle is equal to 3.
