SOLUTION: Please help me solving this question "A footpath a uniform width runs round the inside of a rectangle field 32m long and 24 m wide,if path occupies 208sq.m,find the width of the f

Algebra ->  Human-and-algebraic-language -> SOLUTION: Please help me solving this question "A footpath a uniform width runs round the inside of a rectangle field 32m long and 24 m wide,if path occupies 208sq.m,find the width of the f      Log On


   

Question 827647: Please help me solving this question "A footpath a uniform width runs round the inside of a rectangle field 32m long and 24 m wide,if path occupies 208sq.m,find the width of the footpath. "
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
let x be the width of the footpath and we want to subtract the areas of two rectangles
208 = (32*24) - ((32-2x)*(24-2x))
208 = 768 - (768 -112x +4x^2)
208 = 112x -4x^2
4x^2 -112x +208 = 0
divide both sides of = by 4
x^2 -28x +52 = 0
this expression factors into
(x-2) * (x-26) = 0
we have two solutions for x, namely 2 and 26 BUT we can eliminate 26 since that value is greater than the width of the larger rectangle, now check the answer
x = 2 m
208 = 768 - (28 * 20)
208 = 768 - 560
208 = 208
answer checks