A man built a walk of uniform width around a rectangular pool. If the area of the walk is 407 square feet and the dimensions of the pool are 13 feet by 13 feet

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A man built a walk of uniform width around a rectangular pool. If the area of the walk is 407 square feet and the dimensions of the pool are 13 feet by 13 feet, how wide is the walk?

Answer:

Let width of the walk is x feet then area of walk = (13+2x) * (13+2x) = 407 (given) ------------- (1)
Area of rectangle only = 1313 = 169 ---------- (2)
Subtract equation (2) from equation (1)
(13+2x)^2 – 13
13 = 407 – 169 on manipulation we get quadratic equation
2x^2 +26 x -119 = 169 ------ (3)
It is a quadratic equation find roots by SriDharacharya Formula.
Since it is a length so taking only positive root and discarding the negative value root.
So x = 3.56 feet
So walk is 3.56 feet wide.