a. The length of the side w is 4.6 cm.
b. The perimeter of rectangle A to rectangle B is in the ratio of 1:2.
The area of rectangle A to rectangle B is in the ratio (1:2)² = 1:4.
In the question, we are informed that the two rectangles are in proportion.
This means that the corresponding sides are in proportion.
Thus, we can say that:
(Length of the Rectangle A)/(Length of the rectangle B) = (Width of the Rectangle A)/(Width of the Rectangle B),
or, (6.75 cm)/(13.5 cm) = (2.3 cm)/(w),
or, w = (2.3 * 13.5)/(6.75) cm,
or, w = 4.6 cm.
The ratio of the corresponding sides of rectangle A to rectangle B is 6.75/13.5 = 1:2
The perimeter of the rectangles is also in the same ratio, as the ratio of the corresponding sides of the rectangle.
Thus, the perimeter of rectangle A to rectangle B is in the ratio of 1:2.
The areas of two proportional figures are in the ratio which is equal to the square of the ratio of their corresponding sides.
If we have two figures A and B, and they are proportional, then we can say that:
(Area of A)/(Area of B) = {(Side of A)/(Side of B)}².
Thus, the area of rectangle A to rectangle B is in the ratio (1:2)² = 1:4.
Learn more about proportional figures at
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