If area of a rhombus is 384 cm2 and one of its diagonal is 24 cm, find its perimeter.


Answer:

80 cm

Step by Step Explanation:
  1. We know that the area of the rhombus =  
    Product of diagonals of the rhombus
    2
     
    It is given that one diagonal of the rhombus = 24 cm.
    Let the other diagonal of the rhombus be b cm. Then,
    384 =  
    24 × b
    2
     
    ⇒ 384 × 2 = 24 × b
    ⇒ b =  
    768
    24
     
    ⇒ b = 32
  2. Let us consider one of the right angle triangles formed by the diagonals. Since we know that the diagonals of a rhombus bisect each other, we can say that one of the sides is of length  
    24
    2
     cm = 12 cm and the other side is  
    32
    2
      cm = 16 cm long.
  3. Let the hypotenuse which is the third side of the triangle and also one of the sides of the rhombus be S cm. Then, by the Pythagoras theorem,
    S2 = (12)2 + (16)2
    S2 = 144 + 256
    S2 = 400
    S = √400
    S = 20
  4. Perimeter of the rhombus = 4S
    4 × 20
    = 80
  5. Therefore, the perimeter of the rhombus is 80 cm.

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