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In the figure, $RS ∥ DB ∥ PQ . If CP = PD = 11 cm$ and $DR = RA = 3 cm$ . Then the values of X and Y are respectively.

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12, 10

14, 6

10, 7

16, 8

answer is D.

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Detailed Solution

It is given in the question that in figure

RS ∥ DB ∥ PQ

Also,

CP = PD = 11 cm

and

DR = RA = 3 cm

then we have to find out the value of X and Y resp.
Now in

△ ASR

and

△ ABD

, we have

∠ A = ∠ A

, Common angle in both triangle
We know that

∠ ASR

and

∠ ABQ

because both are corresponding angle b/w parallel lines RS and BD respectively, hence,

∠ ASR = ∠ ABQ

(both are corresponding angle)
Therefore, we can say that

△ ASR ≅ △ ABQ

by AA similarity.
Here AA similarity means Angle-Angle similarity. It means we can say that in

△ ASR

and

△ ABD

, we have

\frac{AR}{AD} = \frac{AS}{AB} = \frac{RS}{DB}

We know that

AR = 3 cm

and

AD = 6 cm

, So on putting these values, we have,

\frac{RS}{DB} = \frac{3}{6} \to \frac{Y}{X} = \frac{1}{2}

On cross multiplication, we get

X = 2 Y

.Now, if we compare this obtained relation

X = 2 Y

, we have only one similar option i.e. option

DX = 16 cm

and

Y = 8 cm

all the other option do not show

X = 2 Y

hus neglected.
Therefore, the correct option is option 4.

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