Question

A rectangular garden is 6 feet by 4 feet. There is a sidewalk of uniform width around the garden. The area of the sidewalk and the garden together is 48 ft2. What is the width of the sidewalk?

Answer 1

Let x be the width of the sidewalk and the area becomes:

A=LW  and L=6+2x and W=4+2x now we have

A=(6+2x)(4+2x) and we are told that A=48ft^2

48=24+20x+4x^2

4x^2+20x-24=0

4(x^2+5x-6)=0

x^2+5x-6=0

x^2-x+6x-6=0

x(x-1)+6(x-1)=0

(x+6)(x-1)=0

So x=-6, 1, however since x is a measurement it must be positive thus

x=width=1 ft is the only possible solution.