3) You are fencing a rectangular puppy kennel with 25 ft of fence. The side of the kennel against your
house does not need a fence. This side is 9 ft long. Find the dimensions of the kennel.
4) A gardener is planning a rectangular garden area in a community garden. His garden will be next to an
existing 12 ft fence. The gardener has a total of 44 ft of fencing to build the other three sides of his garden.
How long will the garden be if the width is 12 ft.
How do you set these 2 problems up?
1. So, don't you just need two equal widths for your rectangle ???
x + x + 9 = 25
Can't get any easier.
4. I can't follow your description. My rectangle has two width of 12 ft, and some length x
x + 12 + 12 = 44
x = 20 , so it overlaps the existing 12 ft fence.
x + x + 9 = 25. The dimensions of the garden are 8 by 9.
To set up these two problems, we need to understand that we have constraints and limited fencing material for each situation.
Problem 3:
1. Let's assume the length of the kennel is L ft.
2. The width of the kennel will be W ft.
3. The length of the kennel that requires fencing will be L - 9 ft (as the side against the house does not need a fence).
4. Since we need a fence on all four sides of the kennel, the total fencing required is 2L + 2W - 9 ft.
5. According to the problem, the total amount of fence is 25 ft, so we can write the equation: 2L + 2W - 9 = 25.
6. Solve the equation to find the dimensions of the kennel.
Problem 4:
1. Let's assume the width of the garden is W ft.
2. The length of the garden that requires fencing will be L ft.
3. The length that needs fencing will be L + 12 ft (as one side is already fenced).
4. The total fencing required will be 2L + W + 12 ft (as there are three sides that need fencing).
5. According to the problem, the total amount of fence is 44 ft, so we can write the equation: 2L + W + 12 = 44.
6. Substitute the given width of 12 ft into the equation, and solve for L to determine the length of the garden.
To set up these two problems, we need to use the information given and set up equations that represent the given conditions.
Let's break down each problem and step-by-step set up the equations:
3) In this problem, we have a rectangular puppy kennel with 25 ft of fence. One side of the kennel, which is against the house, does not need a fence, and it is given that this side is 9 ft long.
Let's assume the width of the kennel is W and the length is L.
Now, we know that the total amount of fence used is 25 ft. Since one side (against the house) does not require a fence, the amount of fence used for the three remaining sides would be:
Amount of fence = Perimeter - length of side against house
25 ft = 2W + L - 9 ft
Here, we have two variables and one equation. To solve for the dimensions of the kennel, we need another equation. Since the problem does not provide any other information, we cannot solve for specific dimensions. However, we can express the length in terms of the width or vice versa using algebraic manipulation.
4) In this problem, we have a rectangular garden area next to an existing 12 ft fence. The gardener has a total of 44 ft of fencing to build the other three sides of the garden. It is given that the width of the garden is 12 ft.
Let's assume the length of the garden is L.
Now, we know that the total amount of fence used is 44 ft. Since one side already has a fence, the amount of fence used for the remaining three sides would be:
Amount of fence = Perimeter - length of side with the existing fence
44 ft = 2W + L - 12 ft
Similar to the previous problem, we have two variables and one equation. To solve for the length of the garden, we need another equation. Since the problem provides the width as 12 ft, we can substitute it into the equation:
44 ft = 2(12 ft) + L - 12 ft
Simplifying this equation, we obtain:
44 ft = 24 ft + L - 12 ft
Combine like terms:
44 ft = 12 ft + L
Subtract 12 ft from both sides:
32 ft = L
Therefore, the length of the garden will be 32 ft, given that the width is 12 ft.