Question

In the adjoining figure, AB is parallel to CD. If OA=3x-19, OB=x-4, OC=x-3 and OD=4, find x.

Answer 1

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.

Hope thse helps u ^_^

Answer 2

SOLUTION

It is given to that ABCD is a Quadrilateral such that AB||CD.

OA = 3x-19

OB= x-4

OC= x-3 and OD= 4

Since, AB||CD

=) ABCD is a trapezium.

We know that the diagonal of a trapezium divide each other proportionally, therefore

=)OA/OC= OB/OD

=)3x-19/x-3 = x-4/4

=)(x-4) (x-3) = 4(3x-19)

=) x^2 -3x -4x+12 -12x +76=0

=) x^2 -19x+88=0

=) x^2 -11x-8x +88= 0

=) x(x-11) -8(x-11) = 0

=) (x-11) (x-8)=0

=) x-11=0. and x-8=0

=) x= 11 and x= 8

hope it helps ✔️