question_answer

How many triangles are there in the following figure?

A) 29                                

B) 23  

C) 19                                

D) None of these

Correct Answer: D

Solution :

The figure may be labelled as shown in the following figure.

It is clear from the figure that there are seventeen triangles in the upper half of the figure \[ABGE=\Delta EIJ,\] \[\Delta EFM,\] \[\Delta AFE,\] \[\Delta HFI,\] \[\Delta FOP,\,\]\[\Delta OBP,\] \[\Delta PBG,\]\[\Delta PGQ,\]\[\Delta PMQ,\] \[\Delta PFM,\] \[\Delta FBM,\] \[\Delta BMG,\]\[\Delta FMG,\]\[\Delta FEG,\]\[\Delta FBP,\]\[\Delta MPG\]and\[\Delta FBG.\]

There are four triangles in the lower half of the figure EGCD \[=\Delta EMD,\,\,\Delta JMK,\,\,\Delta DKL\,\,and\,\,\Delta DMN.\]

There are four four triangle in the main figure ABCD \[=\Delta DBC,\,\,\Delta ADB,\,\,\Delta DPR\,\,and\,\,\Delta HBK\]

Hence, there are a total of 25 triangles in the figure.