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.

Answer 2

The width of sidewalk is 1 feet.

Explanation:

A rectangular garden is 6 feet by 4 feet.

Let sidewalk width be x feet

New length and width of garden including sidewalk width

Length = 6 + 2x

Width = 4 + 2x

Area of sidewalk and garden together is 48

Area of rectangular = L x W

(6+2x)(4+2x) = 48

`4x^2+20x+24=48`

`x^2+5x-6=0`

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

x=-6,1

We will ignore negative 6 because width can't be negative

Hence, The width of sidewalk is 1 feet.