Geometry

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One hundred tiles of a certain size are needed to pave a floor. If a tile, which measures 4 cm less on each side, will be used, 225 tiles will be needed. Find the size of the larger tile.

  • Geometry -

    Let's assume the tiles are square, and each tile is x by x cm
    so area of floor = 100x^2

    then size of each smaller tile = x-4 by x-4

    area with smaller tiles = 225(x-4)^2

    225(x-4)^2 = 100x^2
    take √
    15(x-4) = 10x
    15x - 60 = 10x
    x = 12

    So the larger tile is 12 cm by 12 cm
    (smaller is 8 by 8)

    Check:
    using larger: area = 100(12by12) = 14400 cm^2
    using smaller : area = 225(8by8) = 225(64) = 14400cm^2
    Answer is correct!

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