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.
Please help!
area of the garden = 6000m2
area of the pathway = 3000m2
How do you calculate without the width without length given?
Many thanks
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?
To find the width of the pathway without the length given, you can use the formula for the area of a rectangle:
Area = Length * Width
We know that the area of the garden is 6000m² and the area of the pathway is 3000m². To find the width of the pathway, we can subtract the area of the garden from the total area of the garden and the pathway:
Area of the pathway = Total Area - Area of the garden
So, the width of the pathway can be calculated as follows:
Width of the pathway = (Total Area - Area of the garden) / Length
In this case, the total area is the sum of the area of the garden and the pathway:
Total Area = Area of the garden + Area of the pathway
Let's substitute the given values into the equation:
Total Area = 6000m² + 3000m² = 9000m²
Now we can calculate the width of the pathway:
Width of the pathway = (9000m² - 6000m²) / 120m
Width of the pathway = 3000m² / 120m
Width of the pathway = 25m
Therefore, the width of the pathway is 25 meters.
To find the width of the pathway, we can use the information that the area of the pathway is half of the area of the garden.
First, let's find the area of the garden. The area of a rectangle is calculated by multiplying its length by its width. In this case, the garden has a width of 50 meters and a length of 120 meters, so the area of the garden is:
area of the garden = length × width = 120 m × 50 m = 6000 m²
Since we know that the area of the pathway is half of the area of the garden, we can set up the following equation:
area of the pathway = half of the area of the garden
3000 m² = 1/2 × 6000 m²
To isolate the width of the pathway, we can rearrange the equation:
width of the pathway = (area of the pathway) / (length of the pathway)
width of the pathway = 3000 m² / 120 m
width of the pathway = 25 meters
Therefore, the width of the pathway is 25 meters.
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.