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    Question

    In a rectangle PQRS, a point A is located inside the

    rectangle. The distances from A to three of the rectangle’s vertices are given as follows: AP = 8 cm, AR = 6 cm, and AQ = 5 cm. Determine the length of AS.
    A 5√3 cm Correct Answer Incorrect Answer
    B 3√5 cm Correct Answer Incorrect Answer
    C 5√7 cm Correct Answer Incorrect Answer
    D 5√5 cm Correct Answer Incorrect Answer

    Solution

    Image
    We know that in rectangle,

    AP 2  + AR 2  = AS 2  + AQ 2

    So, 8 2  + 6 2  = AS 2  + 5 2

    Or, 64 + 36 = AS 2  + 25

    Or, 100 = AS 2  + 25

    Or, AS 2  = 75

    Or, AS = ±5√3 cm

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