Question

In the figure, $PS=4cm,SR=2cm,PT=3cm$ and $QT=5cm$.
Calculate $ST$, if $QR=5.8cm$

• A. $2.9cm$
• B. $3.8cm$
• C. $4.9cm$
• D. $5.1cm$

Answer 1

The correct option is A $2.9cm$

Given $PS=4cm,SR=2cm,PT=3cm$ and $QT=6cm$

$\Rightarrow$ $PR=PS+SR=(4+2)cm=6cm$

$\Rightarrow$ $PQ=PT+TQ=(3+6)cm=cm$

$\Rightarrow$ $\frac{PQ}{PS}=\frac{8}{4}=\frac{2}{1}$ ----- ( 1 )

$\Rightarrow$ $\frac{PR}{PT}=\frac{6}{3}=\frac{2}{1}$ ----- ( 2 )

Now, In $△PQR$ and $△PST$

$\Rightarrow$ $\angle RPQ=\angle TPS$ [ Common angle ]

$\Rightarrow$ $\frac{PQ}{PS}=\frac{PR}{PT}=\frac{2}{1}$ [ From ( 1 ) and ( 2 ) ]

$\therefore$ $△PQR\sim △PST$ [ By $SAS$ similarity rule ]

$\Rightarrow$ $\frac{QR}{ST}=\frac{PQ}{PS}=\frac{PR}{PT}$

$\Rightarrow$ $\frac{QR}{ST}=\frac{2}{1}$

$\Rightarrow$ $ST=\frac{QR}{2}=\frac{5.8}{2}=2.9cm$