The perimeter of a rhombus is 74 cm and one of its diagonals is 35 cm. What is the length of other diagonal?


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Answer:

12 cm

Step by Step Explanation:
  1. One way to solve this is as follows:
    We know that,
    a) The sides of a rhombus are equal. Therefore one side =  
    74
    4
      = 18.5
    b) A diagonal of a rhombus divides the rhombus into 2 equal triangles.
    c) The area of a rhombus is  
    1
    2
     (Diagonal1 × Diagonal2) ------(1)
  2. Taking one of the two triangles formed by the diagonal with length 35 cm.
    Area (using Heron's formula) = ^@ \sqrt{ S(S-18.5)(S-18.5)(S-35) } ^@
    Where, S =  
    2 × 18.5 + 35
    2
      =  
    72
    2
      = 36
    Area = ^@ \sqrt{ 36(36-18.5)(36-18.5)(36-35) } ^@ = 210 ------(2)  [The details of this computation are left to the student.]
  3. On comparing equation (1) and (2) we get,
     
    1
    2
     (Diagonal1 × Diagonal2) = 210
    ⇒  
    1
    2
     (35 × Diagonal2) = 210
    ⇒ Diagonal2 = 2 ×  
    210
    35
      = 12 cm

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