Calculus

posted by .

A piece of wire 40 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle.
How much of the wire should go to the square to minimize the total area enclosed by both figures?

  • Calculus -

    let the side of the square be x
    let the side of the triangle be y
    4x + 3y = 40
    x = (40-3y)/4

    height of triangle from the 30-60-90 triangle ratio = √3/2 y
    area of triangle = (1/2)(y)(√3/2 y)
    = (√3/4)y^2

    area of square = [(40-3y)/4]^2
    = (1600 - 240y + 9y^2)/16
    = 100 - 15y + (9/16)y^2

    A = 100 - 15y + (9/16)y^2 + (√3/4)y^2
    dA/dy =-15 + 9/8 y + 2√3/4 y
    = 0 for a max/min

    √3/2 y + 9/8 y = 15
    4√3 y + 9y = 135
    y = 135/(4√3+9) = appr 8.476

    3y = 25.43 m
    then 4x = 14.573 m

    appr 14.57 m should go for the square

    check my arithmetic and algebra

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    A piece of wire 12 m long is cut into two pieces. One piece is bent into the shape of a circle of radius r and the other is bent into a square of side s. How should the wire be cut so that the total area enclosed is: a) a maximum?
  2. calculus

    A five feet piece of wire is cut into two pieces. One Piece is bent into a square and the other is bent into an equilateral triangle. Where should the wire be cut so that the total area enclosed by both is minimum.
  3. math

    A 2 feet piece of wire is cut into two pieces and once piece is bent into a square and the other is bent into an equilateral triangle. How much wire should be used for the square to ensure that the total area enclosed by both shapes …
  4. Calculus

    A piece of wire 40 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut so that the total area enclosed is a maximum= minimum= Find the length …
  5. calculus

    A piece of wire 18 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle. (a) How much wire should be used for the square in order to maximize the total area?
  6. calculus help please

    A piece of wire 14 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximize the total area?
  7. Calculus Help Please Urgent!!!

    A piece of wire 14 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximize the total area?
  8. Calculus

    A wire 7 meters long is cut into two pieces. One piece is bent into a square for a frame for a stained glass ornament, while the other piece is bent into a circle for a TV antenna. To reduce storage space, where should the wire be …
  9. Calc 1

    A piece of wire 11 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximize the total area?
  10. Calculus 1

    A piece of wire 23 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximize the total area?

More Similar Questions