Question

In the given figure, each of PA, QB, RC and SD is perpendicular to $l$. If AB=6 cm, BC= 9 cm, CD = 12 cm and PS = 36 cm, then determine PQ, QR and RS.

Answer 1

$AB=6cm,BC=9cm,CD=12cm$ and $SP=36cm$

From $PA,QB,RC$ and $SD$ are perpendicular to the same line $l$, so they are parallel to each other.

By theorem of intercepts, we have

$\frac{PQ}{AB}=\frac{QB}{BC}=\frac{RS}{CD}=\frac{PS}{AD}$

$\Rightarrow$ $\frac{PQ}{6}=\frac{QR}{9}=\frac{RS}{12}=\frac{36}{27}$

$\Rightarrow$ $\frac{PQ}{6}=\frac{36}{27}$

$\therefore$ $PQ=8cm$

$\Rightarrow$ $\frac{QR}{9}=\frac{36}{27}$

$\therefore$ $QR=12cm$

$\Rightarrow$ $\frac{RS}{12}=\frac{36}{27}$

$\therefore$ $RS=16cm$