width = w
length = w+48.2
P=343.6
the formula for perimeter
P =2(l+w)
substitute what was given in the problem
343.6 = 2(w+48.2 +w)
combine like terms
343.6=2(2w +48.2)
divide by 2
171.8 = 2w+48.2
subtract 48.2 from each side
123.6 = 2w
w = 61.8mm
l = w +48.2
l =61.6+48.2
l=110mm
Answer: width = 61.8mm
length = 110 mm
