Question

In the figure, RS || DB || PQ. If CP = PD = 11 cm and DR = RA = 3cm. Then the values of x and y are
respectively
a) 12, 10
b) 14,6
c) 10,7
d) 16,8​

Answer 1

Answer: option (d) 16, 8

Step-by-step explanation:

Given data:

RS || DB || PQ.  

CP = PD = 11 cm  

DR = RA = 3cm

To find: value of x & y

Solution:

From the figure attached below, considering ∆ASR and ∆ABD, we get

∠ A = ∠ A ….. [Common angle]

∠ARS = ∠ADB ……. [∵ RS//DB, Angle ARS and Angle ADB are corresponding angles]

∴ By AA Simiarity, ∆ASR  ~ ∆ABD

Since the corresponding sides of similar triangles are proportional

∴ AS/AB = SR/BD = AR/AD

Now, taking  

AR/AD = SR/DB

⇒ 3/(3+3) = y/x ….. (given values)

⇒ 3/6 = y/x

⇒ ½ = y/x

⇒ x = 2y ….. (i)

Comparing the eq. (i) with each of the options given in the question, the relation which truly satisfies the eq.(i) x = 2y is option (d) where x= 16 cm & y = 8 cm.

Answer 2

d)16,8 is the correct answer