Question

The length is 4 units less than 3 times the width. The perimeter is 22 units more than twice the width.

Answer 1

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

Answer 2

L = length

w = width

p = perimeter

perimeter = 2L +2W

L = 3w-4

p = 2w+22

so

2w+22 = 2(3w-4) + 2w

2w+22 = 6w-8+2w

2w+22 = 8w-8

2w+30 = 8w

30=6w

w = 30/6 = 5

width = 5 units

Length = 3w-4 = 3*5 = 15-4 = 11

perimeter = 2w+22 = 2*5 =10+22 = 32

check: p = 2L +2w = 2(11) + 2(5) = 22+10 = 32