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

 Feb 12, 2022
 #1
avatar+124594 
+1

The side of the rhombus =  148 / 4    =   37

 

Using the Pythagorean Theorem, half the length  of the other diagonal =   sqrt  [ 37^2  - (28/2)^2 ]  =

sqrt [ 37^2  - 14^2 ] =   sqrt  [ 1173 ] 

 

So the length of the other diagonal is twice this  =   2sqrt [ 1173 ]

 

And the area  =   (1/2) (product of the diagonals ) =  (1/2) ( 28) *2 sqrt (1173)  =  =  28sqrt [ 1173 ]  units^2

 

 

cool cool cool

 Feb 12, 2022
 #2
avatar+251 
+4

You can refer back here.

The numbers may be different but the concpet is pretty much the same.

 Feb 12, 2022

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