Posted by alysa on Monday, January 21, 2013 at 2:29am.
the perimeter of an ellipse with an area equal to 12pi square units if the non opposite vertices are 5units apart
- solid mensuration - bobpursley, Monday, January 21, 2013 at 5:01am
- solid mensuration - Reiny, Monday, January 21, 2013 at 10:00am
What a nasty question.
the area of the ellipse is abπ , where a and b are each 1/2 of the axes
so abπ = 12π --->ab = 6 or b = 6/a
let A(a,0) and B(0,b) be the two adjacent vertices
given AB = 5
√(a^2 + b^2) = 5
a^2 + b^2 = 25
a^2 + 36/a^2 = 25
a^4 + 36 = 25a^2
a^4 - 25a^2 + 36 = 0
a^2 = (25 ± √481)/2 = appr 23.4658 or appr 1.53414
a = 4.844157.. or a = 1.2386... ignoring the 2 negative values
then b = 6/a
if a = 4.844148, then b = 1.2386
if a = 1.2386 , then a = 4.844157
ahhh, summetrical answers
So we basically have the same ellipse, one horizontal, one vertical
The perimeter of an ellipse is one of the most challenging questions dealing with the ellipse.
It requires Calculus and finding the length of a curve.
Here is a link that has some approximation methods
Here is an applet that let's you find all properties of an ellipse
enter the 2a= 9.6883
enter 2b = 2.47721..
and press calculate to get a perimeter of appr. 20.87
Answer This Question
More Related Questions
- 2nd grade math - If you have a rectangle with 24 square units 3 lines down 8 ...
- Algebra 2 - Choose the equation that best represents an ellipse for the given ...
- Analytic Geometry - A square is a quadrilateral with four equal sides. The area ...
- geometry - The area of an ellipse in the form (x*x/a*a)+(y*y)/(b*b)=1 is A=3.14*...
- solid mensuration - A circle has an area equal to 25 pi sq.cm. Its diameter AB ...
- solid mensuration - let a and b be opposite vertices of a unit cube (i.e. , the ...
- Solid Mensuration - The area of a regular hexagon inscribed in a circle is equal...
- solid mensuration - Find the area of a portion of a semicircle of radius 15 m ...
- Calculus - I seriously do not understand anything about this problem Please ...
- Math - A square has an area of 27 square units. If the perimeter of the square ...