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30 March, 23:40

Geoff wants to purchase a circular area rug for his room, but he can't decide between the small size and the large size. A small rug covers an area of approximately 67 square feet. If a large size rug has twice the dimensions of a small rug, how many times larger is the large rug?

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  1. 31 March, 03:12
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    Answer: The larger rug is 4 times larger

    Step-by-step explanation:

    The formula for determining the area of a circle is expressed as

    Area = πr²

    Where

    r represents the radius of the circle.

    π is a constant whose value is 3.14

    The small circular rug covers an area of approximately 67 square feet. This means that

    67 = πr²

    r² = 67/π = 67/3.14 = 21.34

    r = √21.34 = 4.62

    If a large size rug has twice the dimensions of a small rug, it means that the radius of the larger rug would be

    2 * 4.62 = 9.24

    The area of the larger rug would be

    3.14 * 9.24² = 268.06ft²

    Therefore

    268.06/67 = 4

    The larger rug is 4 times larger
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