Area = l w
30 = l w
Perimeter = 2l + 2w
34 = 2l + 2w
Let's get the width from the Area and substitute it in the perimeter
w = 30/l
34 = 2l + 2w
34 = 2l + 2(30/l)
34 = 2l + (60/l)
34 = (2l^2 +60) / l
34l = 2l^2 + 60
17l = l^2 + 30
0 = l^2 - 17l +30
(l-15)(l-2)
l-15 = 0
l=15
l-2 = 0
l = 2
Length can either be 15 or 2
So the dimensions are 15 and 2.
