A \( \Large \Large \triangle DEF \) is formed by joining the mid points of the sides of \( \Large \Large \triangle ABC\). Similarly, a \( \Large \Large \triangle PQR \) is formed by joining the mid-points of the sides of the \( \Large \Large \triangle DEF \). If the sides of the PQR are of lengths 1, 2 and 3 units, what is the perimeter of the \( \Large \Large \triangle ABC \)?

A) 18 units

B) 24 units

C) 48 units

D) Cannot be determined

Correct answer:
B) 24 units

Description for Correct answer:

Perimeter of \( \Large \triangle PQR \) = 1 + 2 + 3 = 6 units



Now,in \( \Large \triangle DEF \),

\( \Large \frac{DQ}{DF}=\frac{1}{2}=\frac{PQ}{FE} \)

so, 2PQ=FE

Similarly, DF = 2PR and DE = 2QR

Perimeter of \( \Large \triangle DEF \) = \( \Large 2\times 6 \) = 12 units

Similarly,

Perimeter of \( \Large \triangle ABC \) = \( \Large 2\times Perimeter \ of \triangle DEF \)

=\( \Large 2\times 12 \)=24 units



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