Gabriel walked 100m around the perimeter playground.How long and how wide could the play ground be? give three different answers.
It could be 25 by 25
or
20 by 30
or
10 by 40
Thank you, Ms.Sue! it was really helpful
To find the possible dimensions of the playground, we need to consider that Gabriel walked 100m around its perimeter. The perimeter of a rectangle is given by the formula P = 2L + 2W, where L represents the length and W represents the width of the rectangle.
Let's consider three scenarios:
1. Assuming the length and width are equal:
In this case, the formula becomes P = 2L + 2L, which simplifies to P = 4L. Since Gabriel walked 100m, we have 100 = 4L. Solving for L gives us L = 25m. Therefore, the playground could be a square with sides measuring 25m.
2. Assuming the length is twice the width:
Let's assume the width is W. In this case, the formula becomes P = 2(2W) + 2W, which simplifies to P = 6W. Since Gabriel walked 100m, we have 100 = 6W. Solving for W gives us W ≈ 16.67m. Therefore, the playground could be a rectangle with a length of approximately 33.33m and a width of 16.67m.
3. Assuming the length is three times the width:
Let's assume the width is W. In this case, the formula becomes P = 2(3W) + 2W, which simplifies to P = 8W. Since Gabriel walked 100m, we have 100 = 8W. Solving for W gives us W = 12.5m. Therefore, the playground could be a rectangle with a length of 37.5m and a width of 12.5m.
So, there are three possible answers for the length and width of the playground:
1. Square: Length = 25m, Width = 25m.
2. Rectangle: Length ≈ 33.33m, Width ≈ 16.67m.
3. Rectangle: Length = 37.5m, Width = 12.5m.