The length of rectangle A is 1/3 the length of rectangle B.The width of rectangle A is twice the width of rectangle B.Find the ratio of the area of rectangle A to the area of rectangle B.
If rectangle B has width x and length y, we have
A/B = (x/3 * 2y)/xy = 2/3
just multiply the scale factors: 1/3 * 2 = 2/3
To find the ratio of the areas of rectangle A to rectangle B, we need to know the formulas for the areas of rectangles. The area of a rectangle is calculated by multiplying its length by its width.
Let's assume the length of rectangle B is L and the width of rectangle B is W. Given that, we can determine the dimensions of rectangle A:
Length of rectangle A = 1/3 * Length of rectangle B = 1/3 * L
Width of rectangle A = 2 * Width of rectangle B = 2 * W
The area of rectangle A is then calculated as:
Area of rectangle A = Length of rectangle A * Width of rectangle A = (1/3 * L) * (2 * W) = 2/3 * L * W
The area of rectangle B is simply:
Area of rectangle B = Length of rectangle B * Width of rectangle B = L * W
Now, to find the ratio of the areas, we divide the area of rectangle A by the area of rectangle B:
Ratio = Area of rectangle A / Area of rectangle B = (2/3 * L * W) / (L * W)
Simplifying the expression, we find:
Ratio = 2/3
Therefore, the ratio of the area of rectangle A to the area of rectangle B is 2/3.