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? A) 1 foot B) 2 feet C) 4 feet D) 6 feet

Answer 1

The width of the sidewalk is 1 feet

Explanation:

We are given

A rectangular garden is 6 feet by 4 feet

Let's assume width of the side of walk is x feet

Since, there is a sidewalk of uniform width around the garden

now, we can find width and height of the garden and side walk

L=6+2x

W=4+2x

now, we can find total area

Total area is

`=L* W`

now, we can plug values

`=(6+2x)* (4+2x)`

The area of the sidewalk and the garden together is 48 ft^2

so, we can set it equal and then we can solve for x

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

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

`4x^2+20x-24=0`

we can factor out 4

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

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

`x=-6,x=1`

we know that dimension can never be negative

so, we will only consider positive

`x=1`