Question:
In the given figure, if \( ST \parallel QR \), \( QS = 3 \text{ cm} \), \( SR = 1.5 \text{ cm} \), and \( PT = 2.8 \text{ cm} \), then find the value of \( TR \).
In the given figure, if \( ST \parallel QR \), \( QS = 3 \text{ cm} \), \( SR = 1.5 \text{ cm} \), and \( PT = 2.8 \text{ cm} \), then find the value of \( TR \).
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In problems involving parallel lines in triangles, use the Basic Proportionality Theorem: ratios of corresponding sides are equal.
Updated On: Nov 6, 2025
- 3 cm
- 1.5 cm
- 1 cm
- 1.4 cm
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The Correct Option is D
Solution and Explanation
Step 1: Concept used (Basic Proportionality Theorem).
According to the BPT (Thales’ Theorem), if a line is drawn parallel to one side of a triangle to intersect the other two sides, it divides those sides in the same ratio.
Step 2: Apply BPT.
\[ \frac{QS}{SR} = \frac{PT}{TR} \]
Step 3: Substitute given values.
\[ \frac{3}{1.5} = \frac{2.8}{TR} \] \[ 2 = \frac{2.8}{TR} \]
Step 4: Solve for \( TR \).
\[ TR = \frac{2.8}{2} = 1.4 \text{ cm} \] Step 5: Conclusion.
Therefore, the value of \( TR \) is \( \boxed{1.4\ \text{cm}} \).
According to the BPT (Thales’ Theorem), if a line is drawn parallel to one side of a triangle to intersect the other two sides, it divides those sides in the same ratio.
Step 2: Apply BPT.
\[ \frac{QS}{SR} = \frac{PT}{TR} \]
Step 3: Substitute given values.
\[ \frac{3}{1.5} = \frac{2.8}{TR} \] \[ 2 = \frac{2.8}{TR} \]
Step 4: Solve for \( TR \).
\[ TR = \frac{2.8}{2} = 1.4 \text{ cm} \] Step 5: Conclusion.
Therefore, the value of \( TR \) is \( \boxed{1.4\ \text{cm}} \).
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