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.