Question

A footpath of uniform width runs all around the inside of the rectangular field 50m long and 38m wide. If the area of the path is 492m2, find its width.

Answer 1

Original area of the field=50*38=1900m^2

Given path of uniform width is inside the field

Let this be of y m width

New inner rectangular field will have length=(50-2y)m

New inner rectangular field will have breadth=(38-2y)m

Given area of the path=492m^2

Therefore,

Original area=new area + path area

1900=492+{(50-2y)*(38-2y)}

1900=492+{1900-100y-76y+4y^2}

1900=492+(1900-176y+4y^2)

4y^2-176y+492=0

4(y^2-44y+123)=0

Solving for the quadratic equation

y^2-41y-3y+123=0

y(y-41)-3(y-41)=0

(y-3)(y-41)=0

y=41 or 3

In this case y=3m