Question

The parallel sides of a trapezoid are $3$ cm and $9$t cm. The nonparallelsides are $4$ cm and $6$ cm. A line parallel to the base divides the trapezoidinto two trapezoids of equal perimeters. The ratio in which each of then on parallel sides is divided, if $\frac{AP}{BQ}=\frac{PD}{QC}$, is ___

• A. $4:3$
• B. $3:2$
• C. $4:1$
• D. $3:1$

Answer 1

Answer: (B)

$3:2$

Let $PQ=p,AP=x,BQ=y$

$ABQP$ and $PQCD$ have equal perimeters

$\Rightarrow AP+PQ+QB+BA=PD+DC+CQ+QP$

$\Rightarrow x+p+y+3=6-x+9+4-y+p$

$\Rightarrow x+y=8$

Since $\frac{AP}{BQ}=\frac{PD}{QC}$

$\Rightarrow \frac{x}{6-x}=\frac{y}{6-y}$

$\Rightarrow 2x=3y$

$\Rightarrow x=\frac{16}{5},y=\frac{24}{5}$

$\Rightarrow \frac{AP}{BQ}=\frac{x}{y}=\frac{3}{2}$