Question

A 20ft by 40ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 396 ft squared, how wide is the walkway

Answer 1

The width of the walkway is: 3 feet

Step-by-step explanation:

Given

Length of pool = 20 feet

width of pool = 40 feet

Let x be the width of the side walkway

Then the length with walkway will be: 20+2x

Width with walkway will be: 40+2x

Then total area with walkway: $(20+2x)(40+2x)$

so,

$Area\ with\ walkway - area\ of\ swimming\ pool=area\ of\ walkway\\(20+2x)(40+2x)-(20)(40)=396\\800+40x+80x+4x^2-800=396\\120x+4x^2=396\\4x^2+120x-396=0$

Dividing both sides by 4

$x^2+30x-99=0\\x^2+33x-3x-99=0\\x(x+33)-3(x+33)=0\\(x+33)(x-3) = 0\\x-3=0 => x=3\\x+33=0 => x=-33$

As the measurement of length cannot be negative, we will only consider the positive value.

Hence,

The width of the walkway is: 3 feet

Keywords: Rectangle, Area

Learn more about area at:

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