Andie is designing a rectangular play space for her dogs. The length of the play space is 7ft. and the width is 6ft. The new space will have a length and width twice the dimensions of the current space. She needs to purchase sod to cover the ground inside the play space. Write and solve an equation that could be used to determine S the amount of sod the new play space will require.
1. What are you trying to find?
2. What do you know?
3. Create a diagram to model this problem.
4. Write an equation based on the diagram you have created. Use the letter S to represent what you are trying to find.
1. We are trying to find the amount of sod (S) that the new play space will require.
2. We know that the length of the current play space is 7ft and the width is 6ft. The new play space will have double the dimensions of the current one.
3. Let's create a diagram to represent the problem:
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| x x |
| x x |
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In the diagram, the current play space is represented by the rectangle, and the new play space is shown inside it with its dimensions being twice as long and wide.
4. Based on the diagram, we can write the equation:
S = 2 * (2 * length of current play space + 2 * width of current play space)
Substituting the known values:
S = 2 * (2 * 7ft + 2 * 6ft)
Simplifying the equation:
S = 2 * (14ft + 12ft)
S = 2 * 26ft
S = 52ft
Therefore, the amount of sod the new play space will require is 52 square feet.