Posted by Jeff on Saturday, March 20, 2010 at 8:08pm.
An isosceles triangle has a vertex at the origin. Determine the area of the largest such triangle that is bound by the function x^2 + 6y = 48.
So, y=8 when x=0 making a vertical side equal to 8. I also determined that there is a zero at =/ the square root of 48, or approximately 6.93. I know that the base of a triangle=bh/2. I also know that two of the sides must be equal. But, I'm not sure where to go from here. Please help !!

Calculus  Reiny, Saturday, March 20, 2010 at 8:35pm
Did you make a sketch ?
The parabola is y = (1/6)x^2 + 8 or x^2/6 + 8
Let P(x,y) and Q(x,y) be the base of the triangle, both P and Q on the parabola in the first and second quadrants.
The the area of the triangle is
A = (1/2)(2x)(y) = xy
= x(x^2/6 + 8)
= x^3/6 + 8x
d(A)/dx = (1/2)x^2 + 8 = 0 for a max of A
x^2 = 16
x = ± 4
so Area = x^3/6 + 8x
= 64/6 + 32
= 64/3 units^2
Answer This Question
Related Questions
 math  an isosceles triangle has a vertex at the origin. Determine the area of ...
 calculus  An isosceles triangle is drawn with its vertex at the origin and its ...
 math  9. An isosceles triangle is drawn with its vertex at the origin and its ...
 Trig  An isosceles triangle has a height of 12.5 m (measured from the unequal...
 Calculus  The area of largest isosceles triangle that can be drawn with one ...
 isosceles triangle  An isosceles triangle is a triangle that has two equal ...
 Math  An isosceles triangle has its vertex at the origin and the ends of its ...
 Geometry  Can anybody help me with this word problem? A homeowner, who loves ...
 Calculus  AN ISOSCELES TRIANGLE IS TO HAVE A PERIMETER OF 64CM. DETERMINE THE ...
 geometry  Theres a circle with an equilateral triangle in the middle. The ...
More Related Questions