Question 857604
a 7cm by 10cm picture is mounted on a board with an equal border surrounding the picture. the area of the board is 208cm.  what is width of border?  helping son with quadratic equations and stumped why answer is 3?


Area of picture = 7*10 = 70 cm^2


Let width be x on either side of length and width

length of board = 10+2x
Width of board = 7+2x

Area of board = 208 cm^2

Area = L*W

(10+2x)(7+2x) = 208

70+20x+14x+4x^2=208

4x^2+34x+70 = 208

4x^2+34x-138=0
/2

2x^2+17x-69=0

2x^2+23x-6x-69=0

2x(x+11.5)-6(x+11.5)=0

(2x-6)(x+11.5)=0

either 2x=6 OR x=-11.5
Ignore negative

2x=6
x= 3 cm

You can solve by squaring method or formula method.

Formula method

Find the roots of the equation by quadratic formula							
							
a=	2	,	b=	17	,	c=	-69
							
b^2-4ac=	289	+	552				
b^2-4ac=	841						
{{{	sqrt(	841	)=	29	}}}		
{{{x=(-b+-sqrt(b^2-4ac))/(2a)}}}							
{{{x1=(-b+sqrt(b^2-4ac))/(2a)}}}							
x1=(	-17	+	29	)/	4		
x1=	3.00						
{{{x2=(-b-sqrt(b^2-4ac))/(2a)}}}							
x2=(	-17	-29	) /	4			
x2=	-11.50						
Ignore negative value							
x=3 cm