Mathematics

Question

help me please someone
help me please someone

1 Answer

  • Step-by-step explanation:

    a scale factor means that every dimension or line in the original object is multiplied with the exact same factor to create a transformed (larger or smaller) new object.

    the area of an object (including a simple form like this rectangle) is always the product of 2 dimensions.

    that means the scale factor is multiplied in twice creating a squared factor for the area of the new object.

    so, yes, therefore the area grows or shrinks with the square of the scale factor.

    FYI - following the same reason, the volume grows or shrinks with the power of 3 of the scale factor.

    1. k=2

    new area = k² × old area = 4 × 12 = 48 square units.

    2. k=5

    new area = k² × old area = 25 × 12 = 300 square units.

    3. k=1

    new area = k² × old area = 1 × 12 = 12 square units.

    4. k=1/4

    new area = k² × old area = 1/16 × 12 = 12/16 = 3/4 square units.

    5. k=1.2

    new area = k² × old area = (1.2)² × 12 = (12/10)² × 12 = (6/5)² × 12 = 36/25 × 12 or 1.44 × 12 = 432/25 = 17.28 square units.

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