Question

In parallelogram $ABCD$, $AB=(3x-4)$ cm, $BC=(y-1)$ cm, $CD=(y+5)$ cm and $AD=(2x+5)$ cm, find the ratio $AB:BC$.
Answer: $41:35$
Mention answer as 1 if true else mention 0 if false

Answer 1

Given, Parallelogram $ABCD$ with $AB$ $=(3x-4)$, $BC$ $=(y-1)$, $CD$ $=(y+5)$, $AD$ $=(2x+5)$
In a parallelogram, opposite sides are equal,
Therefore, $AB$ $=$ $CD$, $BC$ $=$ $AD$.
For $AB=CD$,
$3x-4=y+5$,

$3x-y=4+5$

$3x-y=9$ ......(1)
For $BC=AD$,
Therefore, $y-1=2x+5$

$\Rightarrow y-2x=6$

$\Rightarrow 2x-y=-6$ .....(2)
From (1) and (2), we have
$3x-y=9$
$\Rightarrow 2x-y=-6$
Solving for $x$ and $y$, we get
$x=15$
$\Rightarrow y=36$
Now, $AB$ $=3x-4=41$
$BC$ $=y-1=35$
Ratio of $AB:BC$ $=41:35$.