Mathematics
Grade9
Easy

Question


ABCED is a kite, AB = 5x – 12, AC = 3x – 2 , BE = 4x , CE = 7x -15 , DC = 10 units,
AB, AC, BE, CE, DC are line segment
Find AC.

  1. 11
  2. 12
  3. 13
  4. 14

Hint:

The perpendicular bisector theorem states that any point on the perpendicular bisector is equidistant from both the endpoints of the line segment on which it is drawn.

The correct answer is: 13


    AC = 3x - 2
    By perpendicular bisector theorem.
    AB = AC
    5x – 12 = 3x - 2
    2x = 12 – 2
    x = 10 over 2
    x = 5
    AB = 5 × 5 – 12
    = 25 – 12
    = 13

    Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. T

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