The width of the pool is 10 feet.
The area of rectangle is product of length and breadth.
Let the width be x.
length = 24 + 2x. and breadth = 12 + 2x
We know, area= 1408 ft².
(12 + 2x)(24 + 2x) = 1408
12*24 + 12*2x + 24*2x + (2x)² = 1408
288 + 72x + 4x² = 1408
4x² + 72x + 288 - 1408 = 0
4x² + 72x - 1120 = 0
x² + 18x - 280 = 0
x² - 10x + 28x - 280 = 0
x(x - 10) + 28(x - 10) = 0
(x - 10)(x + 28) = 0
So, x=10, -28.
Hence, the width be 10 feet.
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