| How many triangles are there in the adjacent figure? |
 |
A) 27
B) 23
C) 21
D) 25
Correct Answer: D
Solution :
| [d] The figure in question may be marked at different points as shown in the following figure |
 |
| Smallest triangles |
| \[=\Delta NGQ,\,\,\Delta OHR,\,\,\Delta PDO,\,\,\Delta NDP,\,\,\Delta JIC,\,\,\Delta ICK=6\]Single triangle |
| \[=\Delta EMJ,\,\,\Delta KLF,\,\,\Delta RIF,\,\,\Delta EQI,\,\,\Delta PHI,\,\,\Delta PGI=6\] |
| Triangle formed with two triangles |
| \[=\Delta ADM,\,\,\Delta DBL,\,\,\Delta DNO,\,\,\Delta DQI,\,\,\Delta DRI,\,\,\Delta CJK,\] |
| \[\Delta GHI,\,\,\Delta DEI,\,\,\Delta DIF=9\] |
| Triangles formed with three triangles |
| \[=\Delta ADC,\,\,\Delta DBC=2\] |
| Largest triangles \[=\Delta ABC,\,\,\Delta EDF=2\] |
| \[\therefore \]Total triangles \[=6+6+9+2+2=25\] |
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