Question 66092
    A square picture has a 1-centimeter border around it. Half of the total area of the picture and the border is made up by the border. Use a graph to determine the dimensions of the picture to the nearest tenth centimeter.
    Choices:
    A) 2.4cm by 2.4cm
    B) 4.8cm by 4.8cm
    C) 2cm by 2cm
    D) 4.1 cm by 4.1cm 
BORDER WIDTH = 1 CM
LET PICTURE BE OF SIDE X CM.
AREA OF PICTURE = X^2
HENCE INCLUDING BORDER OF 1 CM ON ALL SIDES, THE SQUARE WILL BE 
OF SIDE (X+1+1)=X+2
AREA OF PICTURE WITH BORDER =(X+2)^2
AREA OF BORDER=(X+2)^2-2X^2
WE GOT
(X+2)^2-X^2=[(X+2)^2]/2= Y SAY
WE CAN SOLVE THIS BY DRAWING GRAPHS OF 
Y=2X^2...AND...........Y=(X+2)^2......... 
{{{ graph( 600, 600, -50, 50, -50, 50, (x+2)^2/2,(x+2)^2-x^2) }}}
WE FIND THAT THE 2 CURVES INTERSECT AT X=4.8 CM
HENCE THE PICTURE WITH BORDER HAS
6.8 CM SIDE AND PICTURE HAS 4.8 CM SIDE.