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
asked by Sandra
  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

Respond to this Question

First Name

Your Response

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