ABCD is a parallelogram whose diagonals AC and BD intersect each other atright angles. If AC = 16cm and BD = 12cm, find AB.
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Step-by-step explanation:
In parallelogram ABCD, AC and BD intersect at right angles. If AC = 16 cm and BD = 12 cm, then AO = OC and OB = OD where O is the point of intersection of AC and BD. O must be the mid point of AC and BD. By Pythagoras theorem, AB = [AO^2+BO^2]^0.5 = [8^2+6^2]^0.5 = 10 cm.
In fact all sides will be 10 cm and ABCD will be a rhombus.
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Answer:
In a parallelogram diagonals bisect each other
AC/2 - 8 cm
BD / 2 - 6 cm
By Pythagoras theorem
AB^2= 100 cm
AB - 10 cm
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