Question

In the adjoining figure given below $ST\parallel QR$, then what is the value of y?

• A. 5
• B. 9
• C. 12
• D. 15

Answer 1

The correct option is B 9

$Since,ST\parallel QR\Rightarrow \frac{PS}{SQ}=\frac{PT}{TR}$ $\text{(by mid-point theorem)}$
$\Rightarrow \frac{PS}{SQ}+1=\frac{PT}{TR}+1$
$\Rightarrow \frac{PS+SQ}{SQ}=\frac{PT+TR}{TR}$ or $\Rightarrow \frac{PQ}{SQ}=\frac{PR}{TR}$
$\Rightarrow \frac{2y}{y-3}=\frac{2y+3}{y-2}$
$\Rightarrow 2y^2-4y=2y^2-6y+3y-9$
$\Rightarrow -4y=-3y-9$
$\Rightarrow y=9$