Question

In the given figure, if $\angle QPR=\angle PSR,PQ=6cm,PS=4cm$ and $RS=2cm,$ then the length of QR is

• A. 5 cm
• B. 2.5 cm
• C. 3 cm
• D. 4.5 cm

Answer 1

The correct option is D 4.5 cm

Given:
∠QPR = ∠PSR, PQ = 6 cm, PS = 4 cm and RS = 2 cm


In $\Delta QPR$ and $\Delta PSR$,
$\angle QPR=\angle PSR$ (Given)
$\angle QRP=\angle PRS$ (Common)
So, $\Delta QPR\sim \Delta PSR$ (AA similarity)
Thus, their corresponding sides are in the same ratio.
i.e., $\frac{PQ}{PS}=\frac{PR}{RS}=\frac{QR}{PR}$
$\frac{6}{4}=\frac{PR}{2}$........(i)
and $\frac{6}{4}=\frac{QR}{PR}$.......(ii)
From (i), PR = 3 cm ..…(iii)
Now, from (ii) and (iii),
$\frac{6}{4}=\frac{QR}{3}$
$QR=\frac{18}{4}=4.5cm$
Hence, the correct answer is option (4).