1.

In fig, if AB ∥ CD. If OA = 3x – 19, OB = x – 4, OC = x - 3 and OD = 4, find x.

Answer»

It’s given that AB∥CD. 

Required to find the value of x.

We know that, 

Diagonals of a parallelogram bisect each other 

So, 

\(\frac{AO}{CO}\) = \(\frac{BO}{DO}\) 

\(\frac{(3x – 19)}{(x – 3)}\)= \(\frac{(x–4)}{ 4}\) 

4(3x – 19) = (x – 3) (x – 4) 

12x – 76 = x(x – 4) -3(x – 4) 

12x – 76 = x2 – 4x – 3x + 12 

-x2 + 7x – 12 + 12x - 76 = 0 

-x2 + 19x – 88 = 0 

x2 – 19x + 88 = 0 

x2 – 11x – 8x + 88 = 0 

x(x – 11) – 8(x – 11) = 0 

∴ x = 11 or x = 8



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