Question 49. Find the number of triangles in the given figure-

(a) 12

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(b) 13

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(d) 15

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Solution

The correct option is D (d) 15
Answer 49. (d) The figure may be labelled as shown.

The simplest triangles are ABF, BIC, CIH, GIH, FGE and AFE i.e. 6 in number.

The triangles composed of two components each are ABE, AGE, BHF, BCH, CGH and BIE i.e. 6 in number.

The triangles composed of three components each are ABH, BCE and CDE i.e. 3 in number.

Hence, the total number of triangles in the figure = 6 + 6 + 3 = 15

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