pre calculus

A piece of wire 20 ft long is cut into two pieces so that sum of the squares of the length of each piece is 202 Sq ft. Find the length of each piece

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
  1. Set x = length of one piece .
    The length of the second piece is 20 - x .
    x^2 + ( 20 - x )^2 = 202
    x^2 + 400 - 40x + x^2 = 202
    2x^2 - 40x + 400 = 202
    Subtract 202 from each side.
    2x^2 - 40x + 198 = 0
    Divide each side by 2
    x^2 - 20x + 99 = 0
    (x - 9)(x - 11) = 0
    So x = 9 or x = 11
    And we can see that our requirements
    are satisfied when the piece lengths are 9 and 11.

    Can someone check my work if I did it correct?

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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? 14 m this

  2. Calculus

    a piece of wire 12 ft. long is cut into two pieces. one piece is made into a circle and the other piece is made into a square. Let the piece of length x be formed into a circle. allow x to equal 0 or 12, so all the wire is used

  3. Calculus

    A wire 60 cm long is to be cut into two pieces. One of the pieces will be bent into the shape of a square and the other into the shape of an equilateral triangle, as shown in the diagram below: a diagram showing a 60 cm wire cut

  4. geometry

    A wire 10 meters ong is to be cut into two pieces. One piece wil be shaped as a square, and the other piece will be shaped as a circle. (piece one is 4x, piece two is 10-4x) a)Express the total area A enclosed by the pieces of

  1. math problem

    A piece of wire 24 cm long is cut into two pieces and each piece is bent to form a square . Find the lenght of each piece of wire in order to maximize the sum of the area of the two squares?

  2. 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? (b) How

  3. math

    a piece of wire 24 ft. long is cut into two pieces. one piece is made into a circle and the other piece is made into a square. Let the piece of length x be formed into a circle. allow x to equal 0 or 24, so all the wire is used

  4. geometry

    how many inches long is the radius of the largest circle that can fit inside a rectangle 18 inches long and 12 inches wide? An 84-cm wire is cut into three pieces. the second piece is 4 cm longer than the first piece and the third

  1. Calculus

    A piece of wire 7 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? B. How much

  2. Math

    A 14 inch board is to be cut into 3 pieces so that the second piece is twice as long as the first piece and the third piece is 4 times as long as the first piece. If x represents the length of the first piece find the lengths of

  3. Calculus

    A piece of wire 15 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle.

  4. Algebra

    A wire 20 cm long is cut into two pieces. The longer piece is 4 cm longer than the shorter piece. Find the length of the shorter piece of wire

View more similar questions or ask a new question.