Suppose the picture of Archimedes measuring 6 cm by 8 cm, has a frame of uniform width with a total area equal to the area of the picture, how wide is the frame?

Answer 1

Area of picture = 48

Area of frame+ picture = 2(48) = 96

(6+x)(8+x) = 96

x^2 +14x + 48 =96

x^2 +14x -48 = 0

x^2 + 14 + 49 = 48+49= 97

x+7 = sqr97

x = sqr97-7

frame+ picture is 6+sqr97-7 = sqr97-1 wide = almost 9 cm

and 8+sqr97-7 = sqr97+1 long= almost 11 cm

It's a little less than 11 by 9 cm