Question

The perimeter of a parallelogram $ABCD=40$ cm, $AB=3x$ cm, $BC=2x$ cm and $CD=2(y+1)$ cm. Find the values of $x$ and $y$.

• A. $x=5$ and $y=4$
• B. $x=4$ and $y=5$
• C. $x=5$ and $y=5$
• D. $x=4$ and $y=4$

Answer 1

The correct option is B $x=4$ and $y=5$

In the parallelogram $ABCD$ side $AB$ and $CD$ are opposite to each other. Opposite sides of parallelogram are equal.

Thus,

$AB=CD$ and $BC=AD$

$\Rightarrow 3x=2(y+1)$

$\Rightarrow 2x=AD$

$\Rightarrow (y+1)=1.5x$

Now, according to the given condition

$AB+BC+CD+AD=40$
$\Rightarrow 3x+2x+2(y+1)+2x=40$

$\Rightarrow 7x+2\times 1.5x$ $=40$

$\Rightarrow 7x+3x=40$

$\Rightarrow x=4$

Simplify further,

$(y+1)=1.5x=1.5\times 4$

$=6$

$\Rightarrow y=5$