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Areas of similar triangles are as the squares of corresponding sides: find a side or height ratio

This type of question, asked 4 times: CDS 2 2018, CDS 1 2019, CDS 1 2021, CDS 2 2026. All 4 questions below, oldest first.

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  1. Question 1

    CDS 2 2018

    83
    The areas of two similar triangles are (7−43)(7 - 4\sqrt{3}) cm2^2 and (7+43)(7 + 4\sqrt{3}) cm2^2 respectively. The ratio of their corresponding sides is

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  2. Question 2

    CDS 1 2019

    45
    Let two lines pp and qq be parallel. Consider two points BB and CC on the line pp and two points DD and EE on the line qq. The line through BB and EE intersects the line through CC and DD at AA in between the two lines pp and qq. If AC:AD=4:9AC : AD = 4 : 9, then what is the ratio of area of triangle ABCABC to that of triangle ADEADE ?

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  3. Question 3

    CDS 1 2021

    78
    Two isosceles triangles have equal vertical angles and their areas are in the ratio 4.84:5.294.84 : 5.29. What is the ratio of their corresponding heights?

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  4. Question 4

    CDS 2 2026

    68
    Consider the following statements : I. The areas of two similar triangles are in the ratio of the squares of the corresponding medians. II. The areas of two similar triangles are in the ratio of the squares of the corresponding heights. Which of the statements given above is/are correct ?

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