In ΔPQR, PQ = PR = 18 cm, AB and AC are parallel to lines PR and PQ respectively. If A is the mid-point of QR, then what is the perimeter (in cm) of quadrilateral ABPC?

PQ = PR = 18 cm and A is the mid point of QR

AB is parallel to PR and AC is parallel to PQ, => BC is parallel to QR and B and C are mid point of PQ and PR respectively.

=> $$\frac{PB}{PQ}=\frac{BC}{QR}$$

=> $$\frac{BC}{QR}=\frac{1}{2}$$

Thus, BC = $$\frac{1}{2}$$ QR

=> PB = PC = BC = $$\frac{18}{2}=9$$ cm

Similarly, AB = AC = BC = 9 cm and ABPC is a parallelogeram.

$$\therefore$$ Perimeter of ABPC = $$4\times9=36$$ cm

=> Ans - (D)