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8 May, 04:23

Given: △EDN∼△LKI, DQ, KO are altitudes, DN=12, KI=4, DQ=KO+6. Find: QN and OI.

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  1. 8 May, 07:23
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    QN = 3√7 OI = √7

    Step-by-step explanation:

    The ratio of corresponding sides DN and KI is 12 : 4 = 3 : 1. The same ratio applies to altitudes DQ and KO. Since the difference between these altitudes is 6 and the difference between their ratio units is 3-1 = 2, each ratio unit must stand for 6/2 = 3 units of linear measure. That is, ...

    DQ = (3 units) ·3 = 9 units

    KO = (3 units) ·1 = 3 units

    Then the base lengths QN and OI can be found from the Pythagorean theorem:

    KI² = KO² + OI²

    4² = 3² + OI²

    OI = √ (16 - 9)

    OI = √7

    QN = 3·OI = 3√7
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