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Question

In triangle PQR, points S and T lie on PQ and PR, respectively, such that ST ∥ QR. If PS : SQ = 4 : 7 and PT = 12 cm, then PR is equal to:

The correct answer is

33 cm

Since ST ∥ QR, by the Basic Proportionality Theorem (Thales), \( \frac{PS}{SQ}=\frac{PT}{TR} \).

\( \frac{4}{7}=\frac{12}{TR}\Rightarrow TR=\frac{12\times7}{4}=21 \) cm.

\( PR=PT+TR=12+21=33 \) cm.

Hence, PR is equal to 33 cm.

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Similar Questions

  1. The ratio of the areas of two similar triangles is 81 : 121. The ratio of their corresponding heights is:

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  3. The sides of two similar triangles are in the ratio 3 : 5. If the area of the smaller triangle is 108 cm2, then find the area of the larger triangle.

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Important Questions from Triangles, Congruence and Similarity

  1. G is the centroid of the equilateral triangle ABC. If AB = 8√ 3 cm, then the length of AG is equal to:

  2. If sides of a triangle are 12 cm, 15 cm and 21 cm, then what is the inradius (in cm) of the triangle?

  3. What is the area of quadrilateral ABCD?

  4. It is given that ΔABC ~ ΔXYZ and Area ΔABC : Area ΔXYZ = 81 : 25. If AB = 18 cm, BC = 10 cm, CA = 15 cm, then what is the side XZ (in cm)?

  5. Sides of two similar triangles are in the ratio 4 ∶ 9. Area of these triangles are in the ratio:

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