rectangle ABCD is similar to rectangle wxyz , with AB corresponding to wx. if AB=24,BC=30 and wx=16 , what is the area of the rectangle wxyz
AB/WX = BC/XY,
24/16 = 30/XY,
24XY = 480,
XY = 480 / 24 = 20.
Area = (WX)(XY) = 16 * 20 = 320.
What is the area of lmn
To solve this problem, we can use the concept of similarity between rectangles.
In similar rectangles, corresponding sides are proportional. We are given that AB corresponds to wx. Since AB = 24 and wx = 16, we can set up the following proportion:
AB/wx = BC/yz
Substituting the given values, we have:
24/16 = 30/yz
Cross-multiplying, we get:
24 * yz = 16 * 30
Dividing both sides by 24, we find:
yz = (16 * 30) / 24
yz = 20
So, the length of yz is 20.
Since the rectangles are similar, their corresponding sides are proportional. Thus, the ratio of their areas is equal to the square of the ratio of their corresponding sides.
The ratio of the length of AB to wx is 24/16 = 3/2.
Therefore, the ratio of the areas of rectangle ABCD to wxyz is equal to (3/2)^2 = 9/4.
Since the area of rectangle ABCD is 24 * 30 = 720, we can find the area of rectangle wxyz:
(area of wxyz) = (area of ABCD) * (ratio of areas)
(area of wxyz) = 720 * (9/4)
(area of wxyz) = 1620
So, the area of rectangle wxyz is 1620 square units.