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Rhombus ABCD  has perimeter 148, and one of its diagonals has length of 24. How long is the other diagonal?

Guest Nov 27, 2018
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(1/4) of the perimeter  = a side length

 

So

 

148 * (1/4)  =  37

 

The side length forms the hypotenuse of a right triangle

And (1/2) of the known diagonal length = 12    forms one leg of this triangle

 

So...using the Pythagorean Theorem, the other leg = 

 

sqr ( 37^2 - 12^2 )   = sqrt ( 1369 - 144) = sqrt ( 1225) = 35

 

And twice this is the length of the other diagonal =  70

 

 

cool cool cool

CPhill  Nov 27, 2018

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