Geometry

 

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

 

The Parallelogram Law states that the sum of the squares of     

the diagonals equals the sum of the squares of the four sides.     

A rhombus is simply a parallelogram with all four sides equal.     

 

d₁² + d₂²  =  4 s²     

d₁² + 20²  = 4 • 37²     

          d₁²  =  (4 • 1369) – 400     

          d₁²  =  5476 – 400     

          d₁²  =  5076     

          d₁¹  =  sqrt(5076)     

          d₁¹  =  71.25     

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