How do I do this?

Question

The perimeter of Rectangle A is 36 units. The perimeter of Rectangle B is 108 units. Write and solve a system of linear equations to find the values of X and Y.

Answer 1

Assuming the rectangles are similar, the sides are in proportion

2L + 2w = 36 ---> L+w= 18 ---> w = 18-L

2(kL) + 2(kw) = 108 for some fixed number constant k

2k (L+w) = 108

2k ( 18) = 108 <--- substitutes L+w=18

36k = 108

k=3

so rectangle B has dimensions 3 times as large