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. 
:
Let x = the length of the base
then
(3x+5) = the height
:
The Area
{{{1/2}}}*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 = {{{4/3}}}
:
:
see if that checks out
{{{1/2}}} * {{{4/3}}} * (3*(4/3)+5) = 
{{{1/2}}} * {{{4/3}}} * 9 = {{{36/6}}} = 6