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 \( TR \). 

• A. 3 cm
• B. 1.5 cm
• C. 1 cm
• D. 1.4 cm

Hint:

In problems involving parallel lines in triangles, use the Basic Proportionality Theorem: ratios of corresponding sides are equal.

Answer 1

The Correct Option is D

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 \( \boxed{1.4\ \text{cm}} \).