Question

In \( \triangle PQR \), \( ST \parallel QR \), \( PQ = 12 \) cm, \( PR = 24 \) cm, and \( SP = 4 \) cm, then \( PT = \)

• A. 8 cm
• B. 6 cm
• C. 12 cm
• D. 10 cm

Hint:

In triangles, use the Basic Proportionality Theorem to find proportional sides when a line is parallel to one side of the triangle.

Answer 1

The Correct Option is A

In \( \triangle PQR \), we are given that \( ST \parallel QR \). According to the Basic Proportionality Theorem (also known as Thales' theorem), if a line is parallel to one side of a triangle and intersects the other two sides, then the two sides are divided proportionally. That is, \[ \frac{PS}{PQ} = \frac{PT}{PR} \] Substitute the given values: \[ \frac{4}{12} = \frac{PT}{24} \] Now, solve for \( PT \): \[ \frac{1}{3} = \frac{PT}{24} \] \[ PT = \frac{1}{3} \times 24 = 8 \text{ cm} \] Thus, \( PT = 8 \) cm.