Mr. Mullett has designed a playground for his 4 kids. This playground is awesome. The playground
equipment is top of the line, multiple slides, swings, climbing wall and the playground area also includes a trampoline. What he doesn’t have is a sidewalk around the playground area. He wants to know how wide his sidewalk can be if he only wants lay 936 ft squared of concrete. Below is a diagram of the playground
area.
Dimensions: 50' by 15' by 15' by 15' by 15' by 30' by 20' by 20'
3. What was the width of Mr. Mulltet's sidewalk
4. If Mr. Mullett bumped up his amount of concrete to 1200 sq ft, what is his new width?
5. How much concrete would would Mr. Mullett have to by if he wanted a sidewalk with a width of 8 ft.?
Better describe the shape. The dimensions given make no sense to me.
its a big horizontal rectangle with a smaller rectangle on the bottom of it
To find the width of Mr. Mullett's sidewalk, we need to consider the total area of the playground and subtract it from the total area of concrete he wants to lay (936 sq ft).
To calculate the area of the playground, we need to find the dimensions of each section and add them together.
Given dimensions: 50' by 15' by 15' by 15' by 15' by 30' by 20' by 20'
Calculate the area of each section:
Area of 50' by 15': 50' * 15' = 750 sq ft
Area of 15' by 15': 15' * 15' = 225 sq ft
Area of 15' by 30': 15' * 30' = 450 sq ft
Area of 20' by 20': 20' * 20' = 400 sq ft
Add up the areas: 750 + 225 + 225 + 225 + 225 + 450 + 400 + 400 = 3170 sq ft
Now, subtract the playground area from the total area of concrete:
936 sq ft - 3170 sq ft = -2234 sq ft
As you can see, the result is negative, which means there is not enough concrete to cover the entire playground area. Therefore, Mr. Mullett cannot lay a sidewalk.
Now, let's try the next question where Mr. Mullett has 1200 sq ft of concrete.
To find the new width of the sidewalk, we need to use the same approach as before. Subtract the total area of the playground (3170 sq ft) from the new total area of concrete (1200 sq ft).
1200 sq ft - 3170 sq ft = -1970 sq ft
Again, the result is negative, indicating that there is not enough concrete to cover the entire playground area, so Mr. Mullett cannot lay a sidewalk.
Lastly, let's calculate the amount of concrete Mr. Mullett would need if he wanted a sidewalk with a width of 8 ft.
To find the area of the sidewalk, we need to subtract the playground area from the total area of concrete.
Desired sidewalk width = 8 ft
New total area of concrete = 936 sq ft
Total area of concrete needed = playground area + sidewalk area
Sidewalk area = (width of playground + 2 * desired sidewalk width) * (length of playground + 2 * desired sidewalk width) - playground area
Let's calculate it:
Sidewalk area = (50' + 2 * 8') * (15' + 2 * 8') - 3170 sq ft
Sidewalk area = 66' * 31' - 3170 sq ft
Sidewalk area = 2046 sq ft - 3170 sq ft
Sidewalk area = -1124 sq ft
Once again, the result is negative, which means there is not enough concrete to cover the entire playground area with a sidewalk width of 8 ft. Mr. Mullett would require additional concrete to achieve that width.