geometry

 

Rhombus ABCD has perimeter 148, and one of its diagonals has length 28. what is the area of ABCD?     

 

The Parallelogram Law states that the sum of the squares of     

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

All a rhombus is, is a parallelogram with the four sides equal.     

 

d₁² + d₂²  =  4 s²     

d₁² + 28²  = 4 • 37²     

          d₁²  =  (4 • 1369) – 784     

          d₁²  =  5476 – 784     

          d₁²  =  4692     

          d₁¹  =  sqrt(4692)     

          d₁¹  =  68.5     

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