Question

In a parallelogram ABCD if AB=2x+5, CD=y+1, AD=y+5 and BC=3x-4 then ratio of AB : BC is

• A. 71 : 21
• B. 12 : 11
• C. 31 : 35
• D. 4 : 7

Answer 1

The correct option is C 31 : 35

In a parallelogram opposite side are congruent

Hence $AB=CD$ and $BC=AD$

Now $2x+5=y+1$ and $3x-4=y+5$

On solving these equations we will get

$2x-y=-4$......($1$)

And $3x-y=9$......($2$)

Now on solving these equation, we will get $x=13$ and $y=30$

Hence $AB=2x+5=2\left(13\right)+5=31$

And $BC=3x-4=3\left(13\right)-4=35$

Hence $AB:BC=31:35$