Let:l = lengthw = widthp = perimeter
Using the information given we can formulate some equations:l = 3w - 4 [1]p = 2w + 22 [2]Because it is a rectangle:p = 2w + 2l [3]
Using the [2] and [3], we can create another equation by setting them equal to each other, we can do this because they are both equivalent to the perimeter (p);So:2w + 22 = 2w + 2lNow, rearange and solve:2l = 22l = 11We can plug this value of l into [1] and solve for w:(11) = 3w - 43w = 15w = 5We can plug this value of w into [2] to get the perimeter:p = 2(5) + 22= 10 + 22= 32
To summarise:
l = 11
w = 5
p = 32
