question_answer

Count the number of triangles in the adjoining figure.

A)  28                               

B)  20                               

C)  23                               

D)  26

Correct Answer: C

Solution :

: Number of triangles In \[\Delta ABC=({{T}_{1}},{{T}_{2}}{{T}_{3}},{{T}_{4}}{{T}_{5}}{{T}_{6}}{{T}_{7}}{{T}_{6}}{{T}_{7}},({{T}_{1}}{{T}_{2}}{{T}_{3}}{{T}_{4}}{{T}_{5}}{{T}_{6}}{{T}_{7}}))=9\] Number of triangles in \[\Delta DEF\]excluding \[{{T}_{6}}\], \[{{T}_{7}}:({{T}_{8}},{{T}_{9}},{{T}_{10}},{{T}_{11}},{{T}_{8}}{{T}_{9}},{{T}_{10}}{{T}_{11}},{{T}_{12}}{{T}_{13}},{{T}_{12}},{{T}_{13}}\] \[{{T}_{14}},{{T}_{15}},({{T}_{6}},{{T}_{8}},{{T}_{10}},{{T}_{12}}{{T}_{14}}),({{T}_{7}}{{T}_{9}},{{T}_{11}}{{T}_{13}},{{T}_{15}}),\] \[{{T}_{6}}\,{{T}_{7}}\,{{T}_{8}}\,{{T}_{9}}\,{{T}_{10}}\,{{T}_{11}}\,{{T}_{12}}\,{{T}_{13}}\,{{T}_{14}}{{T}_{15}})=14\]