Rectangle ABCD is similar to rectangle EFGH. What is the value of s?
A diagram of two rectangles. For rectangle ABCD, side CD is 36 meters long, and side BC is 12 meters long. For rectangle EFGH, side FG is labeled s, and side GH is 9 meters long.
In similar rectangles, the corresponding sides are proportional. Therefore, we can set up the following proportion:
CD / BC = FG / GH
Plugging in the given values, we get:
36 / 12 = s / 9
Simplifying the left side of the equation, we have:
3 = s / 9
To solve for s, we can cross multiply:
3 * 9 = s
27 = s
Therefore, the value of s is 27 meters.
To find the value of s, we can use the property of similar figures, which states that the corresponding sides of similar figures are proportional.
First, let's compare the corresponding sides of the rectangles:
In Rectangle ABCD: CD = 36 meters and BC = 12 meters.
In Rectangle EFGH: FG = s meters and GH = 9 meters.
Since the two rectangles are similar, the ratio of corresponding sides will be the same. We can set up the following proportion:
CD/FG = BC/GH
36/s = 12/9
To solve for s, we can cross-multiply:
12 × s = 36 × 9
12s = 324
Dividing both sides by 12, we get:
s = 27
Therefore, the value of s is 27 meters.
To solve this problem, we need to understand the concept of similarity between rectangles. When two rectangles are similar, it means that their corresponding sides are proportional.
In this case, we have two rectangles, ABCD and EFGH, and we are given the lengths of some of their sides. Let's compare the corresponding sides:
ABCD: CD = 36 meters, BC = 12 meters
EFGH: GH = 9 meters
To find the value of s, we need to set up a proportion between the corresponding sides of the rectangles:
CD/BC = GH/s
Now, substitute the given values:
36/12 = 9/s
To solve for s, cross-multiply:
36s = 108
Divide both sides by 36:
s = 3
Therefore, the value of s is 3 meters.