SOLUTION: what is the perimeter of an ellipse with an area equal to 12pi square units if the non-opposite vertices are 5 units apart?

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Question 939616: what is the perimeter of an ellipse with an area equal to 12pi square units if the non-opposite vertices are 5 units apart?
Answer by laoman(51) About Me  (Show Source):
You can put this solution on YOUR website!
Given area of the ellipse to be 2pi
Let x and y be the adjacent sides of the ellipse as shown in the picture
pi*x*y = 12*pi
i.e. x*y = 12 -------eqn1
Also
Perimeter of ellipse is pi*(x+y)
Given that the distance between the vertices of x and y are 5units apart
This can form a right anglr triangle,
From pythagoras' theorem, x%5E2%2B+y%5E2+=+5%5E2+=+25
Also, to simplify things up here to get our perimeter,
We know that %28x%2By%29%5E2+=+x%5E2%2By%5E2%2B2%2Ax%2Ay
SubStituting values
%28x%2By%29%5E2+=+25+%2B+2%2A12
%28x%2By%29=+sqrt%2849%29
x+y = 7
But perimeter is pi * (x+y)
= 7 * pi
QED