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14 February, 14:37

A rectangular pool 6 meters by 4 meters is surrounded by a walkway of width x meters. At what value of x will the area of the walkway equal the area of the pool?

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  1. 14 February, 14:50
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    The area of walkway equal to the area of poll for x = 0

    Step-by-step explanation:

    Given as:

    The length of the rectangular pool = 6 m

    The width of the rectangular pool = 4 m

    So, The area of rectangular pool = Length * width

    or, The area of rectangular pool = 6 m * 4 m = 24 m²

    Now,

    The pool is surrounded by walkway of x meter width

    So, The new length = 6 + x + x = 6 + 2 x

    And the new width = 4 + x + x = 4 + 2 x

    So, The area of walkway = new length * new width

    Or, The area of walkway = (6 + 2 x) * (4 + 2 x)

    Or, The area of walkway = 24 + 12 x + 8 x + 4 x²

    Or, The area of walkway = 4 x² + 20 x + 24

    Now, ∵ The area of walkway = The area of pool

    So, 4 x² + 20 x + 24 = 24

    or, 4 x² + 20 x = 24 - 24

    or, 4 x² + 20 x = 0

    Or, 4 x (x + 5) = 0

    Or, x = 0, x = - 5

    So, At x = 0 both the area should be equal

    Hence The area of walkway equal to the area of poll for x = 0 answer
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