Algebraic Polynomials

posted by .

I don't know where to go about creating a polynomial equations for the following problem: A piece of wire 52 in. long is cut into two pieces, and then each piece is formed into a square. If the sum of the areas of the two squares is 97 in.^2, how long are the pieces of wire? My attempted starting point is 97 = (1/4(x))^2 + ((1/4)(52-x))^2, but my numbers don't seem to work. Help is appreciated!

  • Algebraic Polynomials -

    Your equation is perfectly correct.
    What did you get for solution?

  • Algebraic Polynomials -

    Once I move numbers around to achieve a trinomial, I have (1/8)x^2 - (13/2)x + 72, I'm just not sure how I would factor that.

  • Algebraic Polynomials -

    Expand
    97 = (x/4)^2 + ((52-x)/4)^2
    to get
    x^2/8-13x/2+72=0
    multiply by 8 throughout to get
    x^2-52x+576=0
    factor and solve for x.
    You should get two positive integers which add up to 52.

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. Related rates

    A piece of wire 10 feet long is cut into two pieces. One piece is bent into the shape of a circle and the other into the shape of the square. How should the wire be cut so that the combined area of the two figures is as small as possible?
  3. 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 for …
  4. math

    A wire 320 in. long is cut into two pieces. One piece is formed into a square and the other into a circle. If the two figures have the same area, what are the lengths of the two pieces of wire (to the nearest tenth of an inch)?
  5. 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?
  6. 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 …
  7. 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 for …
  8. math

    A wire 360 cm long is cut into two pieces. One piece is formed into a square and the other into a circle. If the two figures have the same area, what are the lengths of the two pieces of wire (to the nearest tenth of an centimeter)?
  9. Pre-Cal

    A wire 360 inches long is cut into two pieces. One piece is formed into a square and the other into a circle. If the two figures have the same area, what are the lengths of the two pieces of wire (to the nearest tenth of an inch)?
  10. Calculus

    A 100 inch piece of wire is cut into two pieces. Each piece of wire is used to make a square wire frame. Let x be the length of one piece of the wire. Determine an algebraic representation A(x) for the total area of the two squares.

More Similar Questions