Question

A footpath of uniform width runs all around The inside of a rectangular field is 50m long and38m wide. If the area of the path is 492m2 find its width

Answer 1

Let X = path width. Then 

(2*50*X) + (2*((38 - 2X) * X)) = 492 
100X + 76X -4X^2 = 492 
4X^2 -176X + 492 = 0 
X^2 - 44X + 123= 0 

Using an online quadratic equation solver, the value of X (the path width) is 3 meters wide. 

EDIT 
I corrected the last part of my equation. I forgot to double the width, as I did the first part,The final answer is 3 meters