Question

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

Answer 1

Since all the lines are perpendicular to line $l$

They all are parallel to each other

$⟹$ the segments of lines in between them are proportional.

$⟹\frac{PQ}{AB}=\frac{QR}{BC}=\frac{RS}{CD}=\frac{PS}{AD}\frac{PQ}{6}=\frac{QR}{9}=\frac{RS}{12}=\frac{36}{27}PQ=\frac{4}{3}\times 6=8cmQR=\frac{4}{3}\times 9=12cmRS=\frac{4}{3}\times 12=16cm$