question_answer

A \[\Delta DEF\]is formed by joining the mid-points of the sides of \[\Delta ABC.\]Similarly, a \[\Delta PQR\] is formed by joining the mid-points of the sides of the\[\Delta DEF.\]If the sides of the \[\Delta PQR\]are of lengths 1, 2 and 3 units, then what is the perimeter of the\[\Delta ABC\]?

A) 18 units                        

B) 24 units]

C) 48 units            

D) 50 units

Correct Answer: B

Solution :

Perimeter of \[\Delta PQR=1+2+3=6\,\,\text{units}\]

Now, in \[\Delta DEF\]

\[\frac{DQ}{DF}=\frac{1}{2}=\frac{PQ}{FE}\]

So,       \[2\,\,PQ=FE\]

Similarly, \[DF=2\,\,PR\]

and       \[DE=2QR\]

\[\therefore \]Perimeter of

\[\Delta DEF=2\times 6=12\,\,\text{units}\]

Similarly, Perimeter of \[\Delta ABC=2\times \]Perimeter of\[\Delta DEF\]

\[=2\times 12=24\,\,\text{units}\]