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1 April, 06:07

lenghts of the sides of a rectangular garden are in a ratio 1:2. Line connecting the centers of the adjacent sides of the garden is 20 m long. Calculate the perimeter and the area of the garden.

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  1. 1 April, 08:11
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    perimeter = 107.4 m

    area = 640.82 m²

    Step-by-step explanation:

    The line connecting the the centers of the adjacent sides of the garden is 20 m long. The line is a diagonal that forms an hypotenuse sides of a triangle.

    The length of side of the rectangle has a ratio of 1 : 2. This means one side has a length a meters and the other 2a meters.

    Pythagoras theorem can be use to get a since a right angle is formed due to the diagonal.

    (a/2) ² + (2a/2) ² = 20²

    (a/2) ² + (a) ² = 20²

    a²/4 + a² = 400

    (a² + 4a²) / 4 = 400

    5a²/4 = 400

    cross multiply

    5a² = 1600

    a² = 1600/5

    a² = 320

    square root both sides

    a = √320

    a = 17.88854382

    a ≈ 17.90

    The required length is a = 17.90 m and the other side will be 17.90 * 2 = 35.80 m.

    Area = length * breadth

    area = 17.90 * 35.80 = 640.82 m²

    perimeter = 2 (l + b)

    perimeter = 2 (35.80 + 17.90)

    perimeter = 2 (53.7)

    perimeter = 107.4 m
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