165
Question
How many triangles are there in the figure?
How many triangles are there in the figure?
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Solution
The correct option is D 12
The simplest triangles are ABE, BEF, EFC, COE and AED, i.e., 5 in number.
The triangles composed of two components each are ABF, BCE, ACE and ABD, i.e., 4 in number.
The triangles composed of three components each are AFC and BCD i.e. 2 in number. There is only one triangle ABC composed of five components.
Thus, there are 5 + 4 + 2 + 1 = 12 triangles in the figure.
Hence, the answer is (D).
The simplest triangles are ABE, BEF, EFC, COE and AED, i.e., 5 in number.
The triangles composed of two components each are ABF, BCE, ACE and ABD, i.e., 4 in number.
The triangles composed of three components each are AFC and BCD i.e. 2 in number. There is only one triangle ABC composed of five components.
Thus, there are 5 + 4 + 2 + 1 = 12 triangles in the figure.
Hence, the answer is (D).
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