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square x has an area of 100 square units. Square Y has a perimeter that is half of the perimeter of square x. What is the area of square y?

  • math -

    each side of x is 10 units since it is square
    then each side of y must be 5 units
    and its area is 25 square units

    In fact the ratio of areas of any two similar figures is the square of the linear scale ratio between them.

  • math -

    Square X, s = side
    Area, A = s^2
    100 = s^2
    Take square root of both sides
    10 = s

    Square X, s = side
    Perimeter, P = 4s
    s = 10
    P = 4(10)
    P = 40

    Square Y, s = side
    Perimeter of Sq. Y = 1/2 Sq. X
    Perimeter of Sq X = 40,
    P = 1/2 (40) = 20
    P = 4s
    20 = 4s
    s = 5

    Square Y, side = s
    Area, A = s^2
    s = 5
    A = 5^2
    A = 25 sq units

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