In a rhombus of side 52 cm, one of the diagonals is 40 cm long. Find the length of the second diagonal.


Answer:

96 cm

Step by Step Explanation:
  1. Let ABCD be the given rhombus whose diagonals intersect at O.

    Then, AB=52 cm.

    Let AC=40 cm and BD=2x cm.
    A C D B O 52 cm 20 cm x cm
  2. We know that the diagonals of a rhombus bisect each other at right angles.  OA=12AC=20 cm,OB=12BD=x cm,and AOB=90
  3. From right ΔAOB, we have AB2=OA2+OB2OB2=AB2OA2=[(52)2(20)2] cm2=[2704400] cm2=2304 cm2   x2= 2304x=2304=48 cm.   OB= 48 cm.   BD=2×OB=2×48 cm=96 cm. Hence, the length of the second diagonal is 96 cm.

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