SOLUTION: the height of a triangle is 5cm more than three times the base. if the area of the triangle is 6cm^2, what is the base. A=6cm^2 h=3b+5cm b=? 6cm^2=(1/2) x b x (3b+5cm) I

Algebra ->  Triangles -> SOLUTION: the height of a triangle is 5cm more than three times the base. if the area of the triangle is 6cm^2, what is the base. A=6cm^2 h=3b+5cm b=? 6cm^2=(1/2) x b x (3b+5cm) I      Log On


   

Question 547630: the height of a triangle is 5cm more than three times the base. if the area of the triangle is 6cm^2, what is the base.
A=6cm^2
h=3b+5cm
b=?
6cm^2=(1/2) x b x (3b+5cm)
I keep getting stuck at: 12cm^2 = 3b^2 + (5cm x b)
Per the answer key, the answer is b= (4/3)cm but I am unable to get to the answer from the question, nor the question from the answer as I always get stuck in the same place
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
the height of a triangle is 5cm more than three times the base.
if the area of the triangle is 6cm^2, what is the base.
:
Let x = the length of the base
then
(3x+5) = the height
:
The Area
1%2F2*x(3x+5) = 6
get rid of the fraction, multiply both sides by 2
x(3x+5) = 12
3x^2 + 5x = 12
3x^2 + 5x - 12 = 0
A quadratic equation, we can factor to:
(3x-4)(x+3) = 0
the positive solution, all we want here
3x = 4
x = 4%2F3
:
:
see if that checks out
1%2F2 * 4%2F3 * (3*(4/3)+5) =
1%2F2 * 4%2F3 * 9 = 36%2F6 = 6