Consider the following figure : A E B ~ 1 H---- F D G C What is the number of rectangles which are not squares in the above figure ? (Given that ABCD is a square and E, F, G, H are mid-points of its sides)

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Q: 117 (CAPF/2017)
Consider the following figure : A E B ~ 1 H---- F D G C What is the number of rectangles which are not squares in the above figure ? (Given that ABCD is a square and E, F, G, H are mid-points of its sides)

question_subject: 

Logic/Reasoning

question_exam: 

CAPF

stats: 

0,3,0,0,3,0,0

keywords: 

{'rectangles': [0, 0, 0, 1], 'squares': [0, 0, 1, 0], 'sides': [3, 0, 3, 3], 'figure': [0, 1, 1, 0], 'above figure': [0, 2, 1, 1]}

In the given figure, we have a square ABCD with midpoints E, F, G, and H on its sides. We need to determine the number of rectangles that are not squares in the figure.

Let`s analyze each option:

Option 1: 14 rectangles - We can start by counting the number of small squares in the figure. Each side of the square ABCD has 3 small squares, so there are a total of 9 small squares. Additionally, there are 4 rectangles formed by connecting the midpoints E, F, G, and H. However, this option does not consider other rectangles that can be formed in the figure. Therefore, this option is incorrect.

Option 2: 16 rectangles - This is the correct answer. As mentioned above, there are 9 small squares and 4 rectangles formed by connecting the midpoints. In addition to these, there are 3 more rectangles formed by connecting the corners A, B, C, and D. Therefore, the total number of rectangles is 9 + 4 + 3 = 16.

Option 3: 20 rectangles - This option overcounts the number of rectangles. There are not enough elements in the figure to form 20 rectangles, so this option is incorrect