Question

In the given figure, $PA,QB,RC$ and $SD$ are all perpendiculars to a line $l,AB=6cm,BC=9cm,CD=12cm$ and $SP=36cm$.

Find $PQ,QR$ and $RS$.

Answer 1

SP=36,AB=6,BC=9,CD=12. AD=AB+BC+CD =6+9+12 $\therefore AD=27$ $\frac{PQ}{PS}=\frac{AB}{AD}$

$PQ=\frac{AB\times PS}{AD}=\frac{6\times 36}{27}=8cm$

$\Rightarrow PQ=8cm.$

$\frac{PR}{PS}=\frac{AC}{AD}$

$\Rightarrow$PR=$\frac{AC\times PS}{AD}$=

$\frac{(6+9)(36{)}^4}{21}$

$PR=20=PQ+QRQR+8=20$

$\therefore$ QR=12cm PS=PQ+=QR+RS 36=8+12+RS $\Rightarrow$ RS=16cm $\therefore$ PQ=8,QR=12 and RS=16 cms