Areas of similar triangles MCQs

Q1. A triangle's sides are halved. Its new area is what fraction of the original?

• A.one quarter
• B.one half
• C.unchanged
• D.one eighth

Answer: A. one quarter

Q2. If the side ratio of two similar triangles is 2:3 and the smaller area is 20, the larger area is:

• A.60
• B.45
• C.40
• D.30

Answer: B. 45

Diagnose the question type - a typical math numerical. The data on the table: 2, 3, 20. We are after the quantity the stem asks for. Tool of choice - Larger area = 20 x (3^2/2^2) = 20 x 9/4 = 45. Rearrange it for the unknown before substituting. Numbers in: Larger area = 20 x (3^2/2^2) = 20 x 9/4 = 45. Lock in option B) 45. Trap-watch: option A) '60' fails since 20 x 9/4 = 45, not 60; option C) '40' is wrong because Use the square of the ratio: 45.

Q3. The ratio of areas of two similar triangles equals (NCERT):

• A.the cube of the side ratio
• B.the ratio of sides
• C.1
• D.the square of the ratio of corresponding sides

Answer: D. the square of the ratio of corresponding sides