Question

AB parallel CD, if AO=3X-19,OB=X-4,OC=X-3 and OD=4 Find x

Answer 1

according to the question

In a quadrilateral ABCD, AB || CD

OA = 3x – 19, OB = x – 4, OC = x – 3, OD = 4

To find:

x = ?

AB || CD

ABCD is a trapezium [The diagonals of trapezium divide each other proportionally]

`(3x – 19)/(x – 3)` = `(x – 4)/(4)`

`rArr` (x – 4)(x – 3) = 4(3x – 19)

`rArr` `x^2` – 3x – 4x + 12 – 12x + 76 = 0

`rArr` `x^2` – 19x + 88 = 0 `rArr` `x^2` – 11x – 8x + 88 = 0

`rArr` x(x – 11) – 8(x – 11) = 0 `rArr` (x – 11)(x – 8) = 0

`rArr` x – 11 = 0 or x – 8 = 0

x = 11 units or 8 units. ans

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Answer 2

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Refer The Attachment .

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