SOLUTION: the diagonal of a rhombus measure 8cm and 6cm.what is the length of a side of the rhombus

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Question 972911: the diagonal of a rhombus measure 8cm and 6cm.what is the length of a side of the rhombus
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The diagonals divide the rhombus into 4 congruent right triangles.
Each side of the rhombus is the hypotenuse of one of those triangles.
Each leg of one of those triangles is half of one diagonal,
so their measures are
green%288cm%29%2F2=green%284cm%29 and red%286cm%29%2F2=red%283cm%29 .
According to the Pythagorean theorem, The lengths of the sides of those triangles, are related by
x%5E2=green%284cm%29%5E2%2Bred%283cm%29%5E2 , so
x%5E2=green%2816%29cm%5E2%2Bred%289%29cm%5E2
x%5E2=25cm%5E2
x%5E2=%285cm%5E2%29
highlight%28x=5cm%29