# 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

## 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?

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