Question

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

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

Answer 1

The correct option is C $31:35$

In parallelogram, opposite sides are parallel and equal
$\therefore AB=CD$ and $AD=BC$
$\Rightarrow 2x+5=y+1⟶1$
$\Rightarrow 3x-4=y+5⟶2$
Equation 2-equation 1
$(3x-2x)-4-5=0+4$
$x=13$
Put value of x in 1
$2\left(13\right)+5-1=y$
$y=30$
$\frac{AB}{BC}=\frac{2x+5}{3x-4}=\frac{2\left(13\right)+5}{3\left(13\right)-4}$
$\frac{AB}{BC}=\frac{31}{35}$
$\therefore AB:BC=31:35$