A garden is 50 meters wide and 120 meters long. There is a pathway that runs along the perimeter inside the garden. If the area of the pathway is half of the area of the garden, then the width of the pathway is ....? meters.

Question

Please help!
area of the garden = 6000m2
area of the pathway = 3000m2
How do you calculate without the width without length given?
Many thanks

Answer 1

The width of the pathway is the unknown,
let it be x m

so make a sketch and you will see that
the length of the whole thing is 120 + 2x
and the width is 50+2x

area of the whole thing = (120+2x)(50+2x)
= 4x^2 + 340x + 6000

If the garden area is 6000, and the pathway is also 6000, then
4x^2 + 340x + 6000 = 2(6000)
4x^2 + 340x - 6000 = 0
x^2 + 85x - 1500 = 0

solve this quadratic, it factors.
take the positive answer, and you have the width of the pathway.
Let me know what you get.

Answer 2

A garden is 30 meters wide and 40 meters long. There is a pathway that runs along the perimeter inside
the garden. The area of the pathway is half of the area of the garden. What is the width of the pathway?