If the area of the rhombus is 336 cm2 and one of its diagonals is 14 cm, find its perimeter.


Answer:

100 cm

Step by Step Explanation:
  1. Let ABCD be the given rhombus with AC=14 cm and BD = x cm.



    We know,  Area of rhombus =12× Product of its diagonals 336=12×AC×BD336=12×14×x2×33614=x48=x Thus, the length of diagonal BD=48 cm.
  2. Let the diagonals AC and BD bisect at a point O.
    We know that the diagonals of a rhombus bisect each other at right angles.
    So, AO=12AC and BO=12BD. AO=12×14=7 cm and BO=12×48=24 cm. Also, AOB=90.
  3. Using Pythagous' theorem in right AOB, we have AB2=AO2+BO2AB2=(7)2+(24)2AB2=49+576AB2=625AB=25 cm
  4. Now,  Perimeter of rhombus =4× Length of side =4×AB=4×25=100 cm Thus, the perimeter of the rhombus is 100 cm.

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