**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 = 13*13 = 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.