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Rhombus ABCD has perimeter 148, and one of its diagonals has length 20. How long is the other diagonal?

 Jun 17, 2021
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Perimeter of rhombus = 4 × side = 148                        A                        B

⇒ side = 37 

Consider rhombus ABCD                                                     O

      AB = BC = CD = DA  &  AC ⊥ BD

 AC & BD intersect at O.                                       D                       C

 

BD = 20  so, OB = OD = 10

Since ∠COD = 90             [diagonals of rhombus intersect at right angles]

⇒ OC = 35.6

 

Diagonal AC =  71.2 units 

 Jun 17, 2021

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