Question

The perimeter of a square A is 3 times the perimeter of square B. What is the ratio of the area of square A to the area of square B? Pls I need the workings.

Answer 1

9/1

Step-by Step Explanation:

First, you have to establish patterns for squares; they have equivalent side lengths for all four sides and you know that the area is just one side squared.

You can solve it like this: assuming x is the length of a side for square b, you can say that square b’s perimeter is 4x. knowing that the perimeter of square a is three times that, we can express the perimeter of square a as 3(4x) or 12x. we can now find the side length of square a by dividing the perimeter by 4, which gets you 3x.

so the side length of square b is x and the side length of square a is 3x. we can now find the areas of both by squaring them:

area of square a = (3x)^2 = 9x^2

area of square b = (x)^2 = x^2

we can express this as a ratio now:

9x^2/x^2

simplified, the ratio can be expressed as 9/1 (x^2 cancels out)