SOLUTION: how to find the diagonals of a rhombus with area and side

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Question 816186: how to find the diagonals of a rhombus with area and side
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!

area=2xy
side%5E2=x%5E2%2By%5E2
area%2Bside%5E2=x%5E2%2B2xy%2By%5E2=%28x%2By%29%5E2
Making
b=-sqrt%28area%2Bside%5E2%29=-%28x%2By%29 and
c=area%2F2=xy ,
we can write the equation
z%5E2%2Bbz%2Bc=0 .
The solutions to that equation will be x and y ,
and the diagonals of the rhombus are 2x and 2y .

For example, if side=65 and area=2016 in some units and the corresponding square units respectively,
and
c=2016%2F2=1008 .
Solving the equation
z%5E2-79z%2B1008=0
either by factoring it into
%28z-16%29%28z-63%29=0 or by applying the quadratic formula
and z=63 ,
for a rhombus with diagonals measuring 2%2A16=32 and 2%2A63=126