question_answer

In a triangle ABC, D and E are the midpoints of AB and AC. If the area of AABC = 60 sq cm. then the area of the A ADE is equal to

A)  15 sq cm          

B)         20 sq cm

C)  25 sq cm        

D)         30 sq cm

Correct Answer: A

Solution :

  Referring figure, \[DE=\frac{1}{2}BC\]                 and        \[AP=\frac{1}{2}AQ\] Given, Area of \[\Delta \,ABC=60\,c{{m}^{2}}\] or            \[\frac{1}{2}\times BC\times AQ=60\] or            \[BC\times AQ=120\] \[\therefore \] Area of \[\Delta \,ADE=\frac{1}{2}\,DE\times AP\] \[=\frac{1}{2}\times \frac{1}{2}BC\times \frac{1}{2}AQ=\frac{1}{8}BC\times AQ\] \[=\frac{1}{8}=120=15\,sq.\,cm.\]