In the given figure if $A B | | D C$ find the value of $x$ . If $O A = 3 x - 1$ $P B = 2 x + 1$ $O C = 5 x - 3$ and $O D = 6 x - 5$

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Solution

$\begin{matrix} O A = 3 x - 1 O C = 5 x - 3 O B = 2 x + 1 O D = 6 x - 5 T h e d i a g o n a l s o f t r a p e z i u m d i v i d e e a c h o t h e r p r o p o r t i o n a l l y \frac{O A}{O C} = \frac{O B}{O D} \Rightarrow \frac{(3 x - 1)}{(5 x - 3)} = \frac{(2 x + 1)}{(6 x - 5)} \Rightarrow (3 x - 1) (6 x - 5) = (2 x + 1) (5 x - 3) \Rightarrow 18 x^{2} - 21 x + 5 = 10 x^{2} - x - 3 \Rightarrow 8 x^{2} - 20 x + 8 = 0 \Rightarrow 2 x^{2} - 5 x + 2 = 0 \Rightarrow (2 x - 1) (x - 2) = 0 \Rightarrow x = \frac{1}{2} o r 2 i f w e p u t x = \frac{1}{2} i n O D t h e v a l u e o f O D i s n e g a t i v e H e n c e, x = 2 \end{matrix}$

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Similar questions

A B | | D C

A O = (3 x - 1) c m

O B = (2 x + 1) c m, O C = (5 x - 3) c m

O D = (6 x - 5) c m

A B

D C .

O A = (3 x - 4) c m, O B = (x + 3) c m, O C = 6 c m

O D = 3 c m,

x .

\frac{A O}{O C} = \frac{B O}{O D} = \frac{1}{2}

In figure, $\frac{A O}{O C} = \frac{B O}{O D} = \frac{1}{2}$ and AB = 5cm. Find the value of DC.

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