# Calculus

Find the area of the largest rectangle having one side on the x-axis and inscribed in a triangle formed by the lines y=x, y=0 and 3x+y=20.

1. 👍 0
2. 👎 0
3. 👁 73
1. If the rectangle has height x, then it has vertices

(x,0), (x,x), ((20-x)/3,x), ((20-x)/3,0)

so, its area is
a = x((20-x)/3-x) = 20x/3 - 4x^2/3
da/dx = 20/3 - 8x/3
da/dx=0 at x=5/2, and

a(5/2) = 25/3

1. 👍 0
2. 👎 0
posted by Steve
2. Thank you so much!

1. 👍 0
2. 👎 0
posted by Sandra

## Similar Questions

1. ### Calculus

Hello, could someone please help me with this problem? I'm a little stuck with it. Thanks, Isaac A rectangle is to be inscribed with its base on the x-axis and its other two vertices above the x-axis on the parabola y=9-x^2 (a)

asked by Isaac on November 28, 2011
2. ### calculus

find the area of the largest rectangle having one side on the x axis and inscribed in the triangle formed by the lines y=x, y=0, and 3x + y = 20

asked by eav on November 16, 2012
3. ### calculus

A rectangle with its base on the x-axis is to be inscribed under the graph of y=2-x^2. Find the height of the rectangle if the area is the largest possible area. (Round to the nearest hundreth)

asked by Sarah on November 13, 2011
4. ### calculus

A rectangle with its base on the x-axis is to be inscribed under the graph of y=2-x^2. Find the height of the rectangle if the area is the largest possible area.

asked by Anonymous on March 2, 2008
5. ### AP Calc

A rectangle is inscribed into the region bounded by the graph of f(x)=(x^2-1)^2 and the x-axis, in such a way that one side of the rectangle lies on the x-axis and the two vertices lie on the graph of f(x). What is the maximum

asked by Luke on November 22, 2014
6. ### calculus

Find the dimensions of the rectangle with the largest area that is inscribed inside the parabola y = 16- x^2 and the x-axis

asked by Patrick on November 1, 2012
7. ### ap calc

A rectangle is inscribed into the region bounded by the graph of f(x)=(x^2-1)^2 and the x-axis, in such a way that one side of the rectangle lies on the x-axis and the two vertices lie on the graph of f(x). what is the maximum

asked by Anonymous on November 18, 2014
8. ### Pre-Calc

Here I am again stuck with another geometry type question. Here goes: A rectangle is inscribed between the x-axis and the parabola y=36-x^2 with one side along the x-axis. He drew the picture with the parabola at points (-6,0)

asked by MUFFY on October 3, 2009
9. ### Calculus

I have to find the area of the largest possible rectangle that can be inscribed under the curve y=e^(-x^2) in the first and second quadrants. How do I do this? It is symmetrical, so one could ignore the second quadrant, and work

asked by mat on December 2, 2006
10. ### Calculus

Find the rectangle of largest area that can be inscribed in a semicircle of radius R, assuming that one side of the rectangle lies on the diameter of the semicircle. NOTE: Let L denote the length of the side that lies on the

asked by John on November 7, 2011

More Similar Questions