Math 12A

posted by .

Each side of a square is 20cm. Four points on the sides are joined as shown to form an inner square. What is the minimum area of the inner square?
Can anyone help with this using quadratics? Please!

  • Math 12A -

    If the points are located so that each side is divided into sections of length x and (20-x), then the side (s) of the inner square can be calculated

    s^2 = x^2 + (20-x)^2
    the are of the inner square is thus
    a(x) = s^2 = x^2 + (20-x)^2 = 2x^2 - 40x + 400

    That is just a parabola with vertex at x = 40/4 = 10

    So, the minimum size of the inner square is just 10*10 = 100, or 1/4 the area of the outer square, when its sides are half as long as the outer sides.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. algebra 1

    A high school wrestling mat must be a square with 38-foot sides and contain 2 circles. Suppose the inner circle has a radius of s feet, and the outer circle's radius is 9 feet longer than the inner circle. What is an expression for …
  2. Math word problem

    A small circular pool is enclosed in a square. Find the area inside the square but outside the circle?
  3. math

    if the sides of a square are increased by 5 cm the area of the new square is four times the area of the original square. Find the length of a side of the original square.
  4. physics

    Given that the side of the square has a length b-a, find the area of one of the four triangles and the area of the small inner square. Give the area of one of the triangles followed by the area of the small inner square separated by …
  5. algebra 1

    a diagram below shows an artistic design,] if the length of the outer square is 12" and the length of the inner square is 7" what is the area of the remaining glass when the smaller square is cut form the larger square?
  6. Analytic Geometry

    A square is a quadrilateral with four equal sides. The area of a square is equal to square of its sides. The diagonal of a square is a line segment joining any two non-consecutive side. Find the area of a square and the length of its …
  7. Math

    A square with a side length of 2s has a smaller square inscribed. The vertices of the smaller square are at the midpoints of the sides of the larger square. What is the ratio of the larger square to the area of the smaller square?
  8. MATH HELP

    The side of a square is Three raised to the five halves power inches. Using the area formula A = s2, determine the area of the square. This is the side of the square in fraction(3^5/2) A = 9 square inches A = 15 square inches A = 225 …
  9. Math

    you can draw a square inside another square by placing each vertex of the inner square on one side of the outer square. The large square in this diagram has side length 10 units a) Determine the area of the inscribed square as a function …
  10. geometry

    square 1 has a side length of x, and square 2 has a side length of y. Square 2 is formed by joining the midpoints of the sides of square 1 in order. If x=2, find the ratio of the are of square 1 to the area of square 2

More Similar Questions