Question

How many rectangles similar to this rectangle are there in the following diagram?

• A. $16$
• B. $20$
• C. $24$
• D. $25$

Answer 1

The correct option is C $24$

"Congruent" has to be exactly the same size, but "Similar" allows resizing.
There are $20$ rectangles that are congruent (and so are also similar).
There are also $4$ similar rectangles with twice the dimensions of the given rectangle. These are the rectangles shaded yellow in the below figure.
The main rectangle (that they all fit in) is not similar though, as it is a bit longer than it should be.
So there are $24$ similar rectangles altogether.

Hence, option $C$ is correct.