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In the adjoining figure, $D E ‖ B C,$ the value of $x$ is,

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answer is D.

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Detailed Solution

Given that DE||BC.
In the adjoining figure, DE || BC, find x. - Sarthaks eConnect | Largest Online Education Community

According to the question,

D E ‖ B C

A D = 4 D B = x − 4 A E = x − 3 E C = 3 x − 19

So, by using the basic proportionality theorem,

A D D B = A E E C ⇒ 4 x − 4 = x − 3 3 x − 19 ⇒ 4 3 x − 19 = x − 4 x − 3

⇒ 12 x − 76 = x 2 − 3 x − 4 x + 12 ⇒ 12 x − 76 = x 2 − 7 x + 12 ⇒ x 2 − 19 x + 88 = 0

⇒ x 2 − 11 x − 8 x + 88 = 0 ⇒ x x − 11 − 8 x − 11 = 0 ⇒ x − 11 x − 8 = 0

\Rightarrow x = 11 or x = 8

Substitute 11 for x in

4 x − 4 = x − 3 3 x − 19

to check the condition

A D D B = A E E C

4 11 − 4 ≠ 11 − 3 311 − 19 ⇒ 47 ≠ 814

Again, substitute 8 for x in

4 x − 4 = x − 3 3 x − 19

to check the condition

A D D B = A E E C

4 8 − 4 = 8 − 3 38 − 19 ⇒ 44 = 55 ⇒ 1 = 1

As the value

x = 8

satisfied the condition so the value of

x

would be

8

.
Thus,

x = 8

.
Hence, option 4 is correct.

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