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

Answer:

The width of the sidewalk is 1 feet

Step-by-step 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

$=L\times W$

now, we can plug values

$=(6+2x)\times (4+2x)$

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

$(6+2x)\times (4+2x)=48$

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

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

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

$x=1$