Question : In a triangle PQR, S, and T are the points on PQ and PR, respectively, such that ST || QR and $\frac{\text{PS}}{\text{SQ}} = \frac{3}{5}$ and PR = 6 cm. Then PT is:
Option 1: 2 cm
Option 2: 2.25 cm
Option 3: 3.5 cm
Option 4: 4 cm
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Correct Answer: 2.25 cm
Solution :
Given:
In $\triangle$PQR, QR || ST
$\frac{\text{PS}}{\text{SQ}} = \frac{3}{5}$
Let PS = 3 units, SQ = 5 units
So, PQ = 3 + 5 = 8 units
PR = 6 cm
In ∆ PST and ∆ PQR,
∵ QR | | ST
∵ $\angle$S = $\angle$Q ; $\angle$T = $\angle$R
∴ By AA - similarity,
Here, $\triangle$PST $\sim \triangle$PQR
$\frac{\text{PS}}{\text{PQ}}=\frac{\text{PT}}{\text{PR}}$
⇒ $\frac{3}{8}=\frac{\text{PT}}{6}$
$\therefore$ PT = $\frac{18}{8}=2.25$ cm
Hence, the correct answer is 2.25 cm.
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