Question 126420
an ellipse with center at the origin and horizontal major axis is to fit snugly inside a rectangle that has its longer sides horizontal. the area of the rectangle is 12 square units, and the perimeter is 14 units. find an equation for the ellipse. 
-------------------
Find the length and width of the rectangle:
2(length + width) = 14
l + w = 7
lw = 12
-----------
l=7-w
(7-w)w = 12
-w^2+7w=12
w^2-7w+12=0
(w-3)(w-4) = 0
w = 3, then length = 4
OR
w = 4, then length = 3
---------------------------
The longer side is horizontal so must be 4.
The shorter side must be 3.
--------------------------------
The semi-major axis must be 2.
The semi-minor axis must be 1.5
-----------------------------------
Equation of the ellipse:
x^2/2^2 + y^2/1.5^2 = 1
============================
Cheers,
Stan H.