Question

In the given figure, RS || DB || PQ. 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

Answer 1

Given: RS || DB || PQ. CP = PD = 11cm and DR = RA = 3cm

To find: the value of x and y respectively.

$$\begin{gathered} \mathrm{In}∆\mathrm{ASR}\mathrm{and}∆\mathrm{ABD}, \\ \angle \mathrm{ASR}=\angle \mathrm{ABQ}\left(\mathrm{Corresponding}\mathrm{angles}\right) \\ \angle \mathrm{A}=\angle \mathrm{A}\left(\mathrm{Common}\right) \\ \therefore ∆\mathrm{ASR}~∆\mathrm{ABD}\left(\mathrm{AA}\hspace{0.17em}\mathrm{Similarity}\right) \end{gathered}$$

This relation is satisfied by option (d).

Hence, x = 16 cm and y = 8cm

Hence the result is .