Question
The rectangles in the figure below are similar. Find the value of x.
A smaller rectangle is inside of a larger rectangle. The rectangles share the top left corner. The right side of the larger rectangle is 5. The right side of the smaller rectangle is 3. The top of the smaller rectangle is x. The distance from the right side of the smaller rectangle to the right side of the larger rectangle is 4.
(1 point)
Responses
2.4
2.4
2.7
2.7
6
6
6.7
6.7
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To solve this problem, we can use the concept of similar triangles.
Since the rectangles are similar, the ratio of their corresponding sides will be equal.
Let's denote the length of the top side of the larger rectangle as a, and the length of the top side of the smaller rectangle as b.
We can set up the following proportion:
a/b = 5/3
To find the value of x, we need to find the value of b.
From the given information, we know that a - b = 4.
Solving these two equations, we have:
5/3 = (b + 4)/b
Cross-multiplying, we get:
5b = 3b + 12
Subtracting 3b from both sides, we have:
2b = 12
Dividing both sides by 2, we find:
b = 6
Therefore, the value of x is equal to 6.