Arectangular pool is 12m long and 6m wide. a walkway of uniform width surrounds the pool. if the area of the walkway is 9m squared less than that of the pool, how wide is the walkway?

The walkway is 1.5 m wide.

The area of the pool is 12(6) = 72 m².

Adding a walkway of unknown width, x, around all 4 sides of the pool increases the width by 2x and the length by 2x; thus the area of the entire pool and walkway together would be given by

(12+2x)(6+2x)

We know that the area of just the walkway is 9 m² less than the area of the pool.  This means that:

(12+2x)(6+2x)-72 = 72-9

Multiplying through we have:
12*6+12*2x+2x*6+2x*2x - 72 = 63
72 + 24x + 12x + 4x² - 72 = 63
24x + 12x + 4x² = 63
36x + 4x² = 63

Writing in standard form we have:
4x² + 36x = 63

We want to set it equal to 0 to solve, so subtract 63 from both sides:
4x² + 36x - 63 = 63 - 63
4x² + 36x - 63 = 0

Using the quadratic formula, 



Since a negative width makes no sense, the walkway is 1.5 m wide.

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