Let L = the length of the poster and W = its width. The Perimeter of the poster is:
Perimeter = 160 cm = 2L + 2W [The perimeter of the poster is 160 cm]
Now W/L = 2/3, so W = (2/3)L [The width & length of the poster are in a 2:3 ratio]
Substitute (2/3)L in place of W in the perimeter equation, solve for L:
160 = 2L + 2W [Perimeter equation]
160 = 2L + 2((2/3)L) [Substitute (2/3)L in place of W]
160 = 2L + (4/3)L
160 = (10/3)L
160*(3/10) = L
48 cm = L
Solve for W:
W = (2/3)L
W = (2/3)48
W = 32 cm
CHECK:
160 = 2L + 2W
160 = 2(48) + 2(32)
160 = 96 + 64
160 = 160
CHECK!
