question_answer

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

A) 18 units

B) 24 units

C) 48 units

D) Cannot be determined due to

Correct Answer: B

Solution :

Perimeter of A PQR = 1 + 2 + 3 = 6 units Now, \[\Delta \]DEF, = \[\frac{PR}{DF}=\frac{1}{2}=\frac{PQ}{FE}\] So, 2PQ = FE Similarly, DF = 2PR and DE = 2QP \[\therefore \] Perimeter of \[\Delta \]DEF = 2 x 6 = 12 units Similarly, perimeter of \[\Delta \]ABC \[= 2 \times  Perimeter of\]\[\Delta \]DEF \[= 2 \times  12 =124 units\]