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15 November, 19:57

The larger square garden at Volterra Hall has sides twice as long as the smaller square garden. Together the gardens cover 18,000 square feet. Find the dimensions of each garden.

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  1. 15 November, 20:06
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    The gardens are square. There are two of them. The total is 18000 square feet. There is a relationship between smallest and largest square.

    Development of the Equation.

    Formula for a square = s*s

    The first garden has a side of s

    The larger garden has a side of 2s

    The area of the first garden = s^2

    The area of the 2nd garden = (2s) ^2

    The two areas together are

    s^2 + (2s) ^2 = 18000

    Solve

    s^2 + 4s^2 = 18000 Add the like terms on the left.

    5s^2 = 18000 Divide by 5

    s^2 = 18000/5

    s^2 = 3600 Take the square root of both sides.

    sqrt (s^2) = sqrt (3600)

    s = 60 For the small garden

    2s = 2*s = 2*60 = 120 for the large garden.

    Answers

    Small garden = 60 by 60

    Large garden = 120 by 120

    Check

    Area of the small garden = 60 * 60 = 3600

    Area of the large garden = 120*120 = 14400

    Total Area = 18000 and it checks.
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