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CAT 2005 — QA Question 23

Similarity of TrianglesEasy
Passage / Data

Answer the next 2 questions based on the information given below.

Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at  a speed of 10 km/hr, reaches B and comes back to A at the same speed.

Consider the triangle ABC shown in the following figure where BC = 12 cm, DB = 9 cm, CD = 6 cm and ∠BCD = ∠BAC. What is the ratio of the perimeter of the triangle ADC to that of the triangle BDC?

Answer & solution

  • 7/9

  • B

    8/9

  • C

    6/9

  • D

    5/9

Solution

m ∠BCD = m ∠BAC and B is common to triangles ABC and CBD.

∆ABC is similar to ∆CBD.

AB/CB = BC/BD = AC/CD

AB/12 = 12/9 = AC/6

AB = 16 cm and AC = 8 cm

AD = AB – BD = 16 – 9 = 7 cm

∴ Perimeter of ∆ADC = 7 + 6 + 8 = 21 cm

∴ Perimeter of ∆BDC = 9 + 6 + 12 = 27 cm

∴ Required ratio = 21/27 = 7/9

Hence, option (a).

CAT 2005 QA Q23: Consider the triangle ABC shown in the following figure where BC = 12 cm, DB = 9 cm, CD = 6 cm and ∠BCD = — Solution | TheCATExam