question_answer

The sides of a triangle are 3 cm, 4 cm and 5 cm. The area (in \[c{{m}^{2}}\]) of the triangle formed by joining the midpoints of this triangle is

A) 6                                 

B) 3

C) (c)\[\frac{3}{2}\]           

D) \[\frac{3}{4}\]

Correct Answer: C

Solution :

\[\because \] \[a=3,\] \[b=4\] and \[c=5\,cm\] \[\therefore \] \[\Delta \,ABC\] is a right angled triangle. \[\therefore \] \[ar\,(\Delta ABC)=\frac{1}{2}\times AC\times BC\]             \[=\frac{1}{2}\times 4\times 3=6\,c{{m}^{2}}\] we also know that             \[ar\,(\Delta PQR)=\frac{1}{4}(\Delta ABC)\]             \[=\frac{1}{4}\times 6=\frac{3}{2}\,c{{m}^{2}}\]