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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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