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?

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) (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,
Also, to simplify things up here to get our perimeter,
We know that
SubStituting values

x+y = 7
But perimeter is pi * (x+y)
= 7 * pi
QED
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