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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.
Options
12, 10
14, 6
10, 7
16, 8
Solution
Given: RS || DB || PQ. CP = PD = 11cm and DR = RA = 3cm
To find: the value of x and y respectively.
\[In ∆ ASR and ∆ ABD, \]
\[\angle ASR = \angle ABQ \left( \text{Corresponding angles} \right)\]
\[\angle A = \angle A \left( \text{Common} \right)\]
\[ \therefore ∆ ASR ~ ∆ ABD \left( AA \hspace{0.167em} \text{Similarity} \right)\]
`(AR)/(AD)=(AS)/(AB)=(RS)/(DB)`
`3/6=(RS)/(DB)`
`1/2=x/y`
`x=2y`
This relation is satisfied by option (d).
Hence, x = 16 cm and y = 8cm
Hence the result is `d`
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