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Similar triangles with given areas and one side: find the corresponding side

The same question, asked 2 times: 15 Nov 2020 Tier II*, 8 Aug 2022 Tier II. Every wording below, oldest first.

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  1. Question 1

    15 Nov 2020 Tier II

    30
    Given that Δ\DeltaDEF~Δ\DeltaABC. If the area of Δ\DeltaABC is 9 cm2\text{cm}^2 and that of Δ\DeltaDEF = 12 cm2\text{cm}^2 and BC = 2.1 cm, then the length of EF is:

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  2. Question 2

    8 Aug 2022 Tier II

    68
    Triangle BAC is similar to triangle PQR. The area of triangle BAC and triangle PQR is 25 cm225\ \text{cm}^2 and 36 cm236\ \text{cm}^2 respectively. If BA =4 cm, then what is the length of PQ?

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