# calculus

posted by .

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 -

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
= (x/2)(5-(1/5)x^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 tried x = 3 and x = 2.8 and they both gave me slightly smaller areas)

• Correction - calculus -

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, ...)

## Similar Questions

1. ### Calculus

An isosceles triangle, whose base is the interval from (0,0) to (c,0), has its vertex on the graph of f(x)=12-x^2. For what value of c does the triangle have maximum area?
2. ### Calculus

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 …
3. ### math

9. 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 Find the area of the largest such triangle.
4. ### Calculus

The area of largest isosceles triangle that can be drawn with one vertex at the origin and with others on a line parallel to and above the x-axis and on the curve y=27-x^2 is.... A) 108 B) 27 C) 12 root 3 D) 54 E) 24 root 3
5. ### math

an isosceles triangle has a vertex at the origin. Determine the area of the largest such triangle that is bound by the function x squared + 6y = 48 and explain why this is infact the maximum area.
6. ### calculus

A rectangle is inscribed in an isosceles triangle. If the sides of the triangle are 10, 10 and 12, what are the dimensions of the rectangle having the greatest area?
7. ### calculus

5. Let for and f(x)=12X^2 for x>=0 and f(x)>=0 a. The line tangent to the graph of f at the point (k, f(k)) intercepts the x-axis at x = 4. What is the value of k?
8. ### Math

An isosceles triangle has its vertex at the origin and the ends of its base on the parabola y=9-x^2. Express the area of the triangle as a function of the length of its base. Assume its base lies above the x-axis.
9. ### geometry

Each base of an isosceles triangle measures 42 degrees, 30'. The base is 14.6 meters long. a. Find the length of a leg of the triangle b. Find the altitude of the triangle c. What is the area of the triangle?
10. ### Precalculus

The sides of an isosceles triangle are 10 cm, 10 cm, and 12 cm. A rectangle is inscribed in the triangle with one side on the triangle's base. The other two vertices of the rectangle are on the triangle's legs. Find the Maximum Area …

More Similar Questions