stumped by english:  Just using common sense, no real math required, I can tell you that the width of the border is 1M. Think about it. If there was no border, just the 5 X 3 rug, then the area (Length X Width) would be 15. Just add 1 to both the 5 and 3 to make it 6 X 4. 6 times 4 equals 24, which is the area you're looking for. (You're not going for an area of 48, that M^2 is just a unit of measurement for area. Just plug in 24 instead.)
2007-12-12 19:31:24

rooster1981:  let x : width of the border
total length of the rug : 2x + 5
total width of the rug : 2x + 3
area : width * length

area:
(2x + 5) (2x + 3) = 24

find x:
(2x + 5) (2x + 3) = 24
4x^2 + 16x + 15 = 24
4x^2 + 16x - 9 = 0
(2x - 1) (2x + 9) = 0

so either 2x - 1 = 0 or 2x + 9 = 0
if 2x - 1 = 0
2x - 1 + 1 = 0 + 1
2x = 1
2x/2 = 1 / 2
x = 0.5
so the border is 0.5 m wide

if 2x + 9 = 0
2x - 9 - 9 = 0 - 9
2x = -9
2x/2 = -9/2
x = -4.5 m
(lengths cannot be negative so this isn't the answer)

to check:

[5 + (0.5 * 2)] * [3 + (0.5 * 2)] = 24
(5 + 1) * (3 + 1) = 24
6 * 4 = 24
24 = 24 OK!
2007-12-12 19:35:09