A garden measuring 12m by 16m is to have a pedestrian pathway installed all around it. The pathway and the garden have a total area of 285m^2. What will be the width of the pathway? (Please explain as you go)
Let the width of sidewalk be x
..
Length of garden = 16 m
Width =12m
285-96=189 m^2
Area =96m^2
Area of sidewalk =189 m^2
Length of ground + sidewalk =16
width of ground + sidewalk = 12+2x
( 16+2x )(12+2x )-189=96
192+32x +24x+4X^2-189 = 96
Also the pathway is the same width all the way around the garden.
I don't get it well
To solve this problem, we first need to determine the area of the garden without the pathway. Then, we can subtract this area from the total area of the garden and the pathway to find the area of just the pathway. Finally, we can calculate the width of the pathway.
Step 1: Find the area of the garden without the pathway
The garden has a length of 12m and a width of 16m, so the area of the garden can be calculated by multiplying these two dimensions:
Area of the garden = length × width = 12m × 16m = 192m^2
Step 2: Calculate the area of just the pathway
The total area of the garden and the pathway is given as 285m^2. Since we know the area of the garden is 192m^2, we can subtract this from the total area to get the area of just the pathway:
Area of the pathway = Total area - Area of the garden
Area of the pathway = 285m^2 - 192m^2 = 93m^2
Step 3: Determine the width of the pathway
Since the pathway surrounds the garden on all sides, the width will be the same on all sides. We can assume the width of the pathway as "x" meters. The garden dimensions (length and width) will be increased by 2x (one x on each side) to include the pathway.
So, the new length of the garden including the pathway will be 12m + 2x meters, and the new width will be 16m + 2x meters.
The area of the garden including the pathway can be calculated by multiplying the new length and width:
Area of the garden including the pathway = (12m + 2x) × (16m + 2x)
But we know that the area of the garden including the pathway is 285m^2. So, we can equate this to the calculated area and solve for x:
(12m + 2x) × (16m + 2x) = 285m^2
Now, we can solve this equation to find the value of x.