Question

In the following figure, $ABCD$ is a parallelogram. Find the values of $x$.

• A. $3$
• B. $5$
• C. $7$
• D. $9$

Answer 1

Answer: (B)

$5$

Given: $ABCD$ is a $\parallel gm$, therefore

$AB=CD$ and $AD=BC$ [Opposite sides of $\parallel gm$ are equal]

$4x=6y+2\Rightarrow 4x-6y=2$

$2x-3y=1\to \left(1\right)$

& $4y=3x-3\Rightarrow 3x-4y=3\to \left(2\right)$

Multiply (1) by 3 and (2) by 2 and subtracting we get,

$6x-9y=3$

$6x-8y=6$

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$0-y=-3$

$y=3$

From (1), $2x-3\times 3=1$

$\Rightarrow x=\frac{9+1}{2}=5$