Similarity, BPT, Pythagoras, area ratios MCQs

Q1. ABC is right-angled at C. CD is the altitude from C onto AB. If AD = 4 and DB = 9, the length CD equals:

• A.6
• B.5
• C.13/2
• D.√13

Answer: A. 6

Reading the problem, 4, 9 (math, chapter 'Triangles'). Our target: the unknown asked. From the chapter we use the relation: Geometric-mean relation CD² = AD·DB = 36, so CD = 6. The arithmetic is: Geometric-mean relation CD² = AD·DB = 36, so CD = 6. Trap: 13/2 takes arithmetic mean. That lands on option A) 6.

Q2. Two triangles have a common vertex and their bases lie on the same line. The ratio of their areas equals:

• A.Ratio of their bases
• B.Square of base ratio
• C.Ratio of their other sides
• D.Always 1:1

Answer: A. Ratio of their bases

The idea this question leans on: Common altitude from common vertex; area ∝ base. Hence the answer is A) Ratio of their bases.

Q3. In triangle PQR, M and N are midpoints of PQ and PR respectively. The ratio [PMN]:[trapezium MQRN] equals:

• A.1:3
• B.1:2
• C.1:4
• D.2:3

Answer: A. 1:3