# 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

1. 👍 0
2. 👎 0
3. 👁 341
1. D) 54

One vertex is x,y and the other is -x,y
y= 27 - x^2

A= 1/2 BxH

B = x - -x = 2x
H = 27 - x^2

A = 1/2 * 2x * (27 - x^2)
Take the derivative, find when the derivative is = 0 then plug that back in to get dimensions and solve for area.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Math

1. Which of the following best describes the altitude of a triangle? A) A segment perpendicular to a side of the triangle. B) A segment that passes through the midpoint and is perpendicular to a side of a triangle. C) A segment

2. ### math

An isosceles triangle has a base of 20 cm. The vertex angle is 82 . Find the length of Each of the two equal sides of the triangle.

3. ### Math

The figure shows two triangles on the coordinate grid: A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A triangle ABC is shown with vertex A on ordered pair

4. ### Maths

Isosceles triangle $ABE$ of area 100 square inches is cut by $\overline{CD}$ into an isosceles trapezoid and a smaller isosceles triangle. The area of the trapezoid is 75 square inches. If the altitude of triangle $ABE$ from $A$

1. ### Math

Can someone please check to see if I answered these true and false statements correctly? Thank you! 1. A triangle can have two right angles. (TRUE??) 2. An equilateral triangle is also an acute. (TRUE??) 3. A right triangle can

2. ### Geometry

The two vertices that form the base of an isosceles triangle are (-5, 3) and (2, 3). What are the coordinates of the other vertex?

3. ### math

Two vertices of a triangle lie on some line. The third vertex belongs to the line that is parallel to the first one. Prove the area of that triangle does not depend on the position of the third vertex on the line.

4. ### math

The figure below is not drawn to scale. The ratio of the triangle ABC to the area of triangle DEC to the area of the triangle FGH is 7:5:3. If 20% of the area of triangle DEC is shaded, what percentage of the figure is unshaded?

1. ### Math-CHECK PLEASE

Which of the statements is ALWAYS TRUE? A-A right triangle is a scalene triangle. B-An equilateral triangle is an isosceles triangle. C-An isosceles triangle is an obtuse triangle. D-A right triangle is an acute triangle. I got