Question

In 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

Given, AB =6cm, BC = 9cm, CD = 12cm and SP = 36cm
Also, PA, QB, RC and SD are all perpendiculars to line l.
$\therefore$ PA II QB II RC II SD
By basic proportionality theorem,
PQ:QR:RS = AB:BC:CD
= 6:9:12
Let PQ = 6x, QR = 9x and RS = 12x
Since, length of PS = 36km
$\therefore$ PQ + QR + RS = 36
$\Rightarrow$ 6x + 9x + 12x = 36
$\Rightarrow$ 27x = 36
$\therefore$ $x=\frac{36}{27}=\frac{4}{3}$
Now, $PQ=6=6\times \frac{4}{3}=8cm$
$QR=9x=9\times \frac{4}{3}=12cm$
and $RS=12x=12\times \frac{4}{3}=16cm$