Question 785757
"The area of a triangular sheet of paper is 28 square inches. One side of the triangle is 2 inches more than three times the length of the altitude to that side. Find the length of that side and the altitude to that side."


area of triangle = 28 jn^2

altitude=x
side = 3x+2

Area of Triangle = ?12 * base * altitude

28= 1/2 * x*(3x+2)

*2
56=x(3x+2)

56=3x^2+2x

3x^2+2x-56=0

Find the roots of the equation by quadratic formula							
							
a=	3	,	b=	2	,	c=	-56
							
b^2-4ac=	4	+	672				
b^2-4ac=	676						
{{{	sqrt(	676	)=	26	}}}		
{{{x=(-b+-sqrt(b^2-4ac))/(2a)}}}							
{{{x1=(-b+sqrt(b^2-4ac))/(2a)}}}							
x1=(	-2	+	26	)/	6		
x1=	4.00						
{{{x2=(-b-sqrt(b^2-4ac))/(2a)}}}							
x2=(	-2	-26	) /	6			
x2=	-4.67						

ignore negative value

altitude = 4

base = 3x+2=> 3*4+2=14

CHECK

1/2 * 4*14
=28