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