The length of rectangle A is 1/3 of the length of rectangle B.Find the ratio of the area of rectangle A to the area of rectangle B?

assuming the rectangles are similar, if the lengths are in the ratio 1:3 then the areas will be in the ratio 1:3^2 = 1:9

To find the ratio of the area of rectangle A to the area of rectangle B, we need to know the formula for the area of a rectangle. The formula for the area of a rectangle is:

Area = Length x Width

Given that the length of rectangle A is 1/3 of the length of rectangle B, we can represent this relationship as:

Length of A = (1/3) x Length of B

Let's say the width of both rectangles is the same. We can represent the width of both rectangles as "W".

So, the length of rectangle A would be (1/3) x Length of B, and the area of rectangle A would be:

Area of A = (1/3) x Length of B x W

Similarly, the length of rectangle B is the full length of rectangle B, and the area of rectangle B would be:

Area of B = Length of B x W

Now, the ratio of the area of rectangle A to the area of rectangle B can be calculated by dividing the area of A by the area of B:

Ratio = (Area of A) / (Area of B)
= [(1/3) x Length of B x W] / (Length of B x W)

Simplifying the expression, we can cancel out the "W" term:

Ratio = (1/3) x Length of B / Length of B
= 1/3

Therefore, the ratio of the area of rectangle A to the area of rectangle B is 1/3.