Posted by nesri on Tuesday, October 5, 2010 at 8:07am.
An isosceles triangle is drawn with its vertex at the origin and its base parallel to the x-axis. The vertices of the base are on the curve 5y=25-x^2 Find the area of the largest such triangle.
- calculus - Reiny, Tuesday, October 5, 2010 at 9:28am
your parabola is y = 5 - (1/5)x^2
let the points of contact of the base of the triangle be (x,y) and (-x,y)
Then the area is
Area = xy/2
= 5x/2 - (1/10)x^3
d(Area)/dx = 5/2 - 3x^2/10
= 0 for a max of Area
3x^2/10 = 5/2
x^2 = 25/3
x = ± 5/√3 or appr. 2.88675
sub back in area expression
I had appr. 4.81125
( I tried x = 3 and x = 2.8 and they both gave me slightly smaller areas)
- Correction - calculus - Reiny, Tuesday, October 5, 2010 at 9:45am
The base of the triangle should have been 2x, which makes the
Area = xy
= 5x - (1/5)x^3
Can you figure out how that changes the answers?
(hint: one stays the same, ...)
Answer This Question
More Related Questions
- math - 9. An isosceles triangle is drawn with its vertex at the origin and its ...
- Calculus - The area of largest isosceles triangle that can be drawn with one ...
- Math - An isosceles triangle has its vertex at the origin and the ends of its ...
- Calculus - An isosceles triangle has a vertex at the origin. Determine the area ...
- calculus - A rectangle is inscribed in an isosceles triangle. If the sides of ...
- Calculus - Hello, could someone please help me with this problem? I'm a little ...
- math - What is the area of the largest rectangle with lower base on the x-axis ...
- algebra - What is the area of the largest rectangle with lower base on the x-...
- math - Show that if a rectangle has its base on the x-axis and two of its ...
- Calculus - An isosceles triangle, whose base is the interval from (0,0) to (c,0...