A garden measuring 12 meters by 6 meters is going to have a walkway constructed all around the perimeter, increasing the total area to 160 square meters. What will be the width of the pathway? (The pathway will be the same width around the entire garden).

Pls Show Work

x=2 meters

Step-by-step explanation:

length = 12+2x

width = 6+2x

Area = (12+2x) (6+2x) = 160

Foil

 72 + 12x+24x+4x^2 = 160

Combine like terms

4x^2 + 36x +72 = 160

Subtract 160 from each side

4x^2 +36x -88 =0

Divide by 4

x^2 +9x -22=0

Factor

What 2 numbers multiply to -22 and add to 9

11 * -2 = -22

11+ -2 = 9

(x +11) (x-2) =0

Using the zero product property

x=-11  x=2

Since we cant have negative length

x=2

the answer is 48m^2!

step-by-step explanation: