In Fig. 4.245,. If CP = PD =11 cm and DR = RA = 3 cm. Then the values of x and y are respectively
A. 12, 10

B. 14, 6

C. 10, 7

D. 16, 8

Given in figure RS || DB || PQ, CP = PD = 11 cm and DR = RA = 3 cm.

In ΔASR and ΔABD,

∠ASR = ∠ABD [corresponding angles]

∠ARS = ∠ADB [corresponding angles]

∠A = ∠A [common]

We know that AAA similarity criterion states that in two triangles, if corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar.

∴ ΔASR ~ ΔABD

We know that two triangles are similar if their corresponding sides are proportional.

∴ x= 2y

∴ x = 16 cm and y = 8 cm