Remark
This question does have a trick in it. It is going to be very difficult to come up with a general solution for any quadrilateral. Because of your grade level, I think the question would be satisfied with any solution at all. That said, I think the easiest way to do this is to use a square.
Solve the perimeter of a small square.
Let each side = 3
Then the perimeter = 4*3
P = 12
Solve the Perimeter of the larger square
Let each side = 4
Then the Perimeter = 4*4
P = 16
What is the ratio of the perimeters of both squares?
P_small / P_ large = 12 / 16 = 3/4
That means that the perimeters are in the ratio of the given conditions.
Note
15/20 is the same thing as 3/4.
Second condition.
Find the area of both squares.
Small square = s^2
A_small_square = 3 * 3 = 9
Area Large Square = 4*4
Area of the Large Square = 16
Ratio of the Areas = A_s/A_L = 9 / 16
Answer
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