A concrete border is to be built around a triangular flower garden that has sides of 10 m, 7 m, and 8 m. The border is to be a straight walking path 1 m wide on all sides of the garden. Before the concrete can be poured, wooden formes need to be placed on the inside perimeter and on the outside perimeter of the border. Determine the total length of wood needed to build the forms.
The answer says 36.22 m. How did they get that?
I can tell that answer is wrong. The wood alone on the inside perimeter will be 10+7+8 =25 m. The outside will be larger than that, so it is over 50 m needed. If I have time later, I will guide you through the solution. It begs for a sketch pad,because you have many similar triangles at the corners. I may give up on it here.
Ughhh
That's exactly what I thought, but my math teacher was being an and insisting it to the level of retardation.
I'm sorry to hear that your math teacher was being difficult. Sometimes, teachers can get caught up in their own ways of solving problems and may not be open to different approaches. However, let's try and solve this problem together.
To find the total length of wood needed to build the forms, we need to calculate the sum of the perimeters of the inside and outside borders.
The perimeter of the triangular flower garden can be found by adding the lengths of its three sides. So, the perimeter of the garden is 10 + 7 + 8 = 25 m.
Since we want to build a 1 m wide path on all sides of the garden, we need to add 1 m to each side of the triangle. So, the new lengths of the sides are 10 + 2(1) = 12 m, 7 + 2(1) = 9 m, and 8 + 2(1) = 10 m.
Now, let's calculate the perimeter of the outside border. Just like before, we'll add the lengths of the three sides: 12 + 9 + 10 = 31 m.
To find the total length of wood needed, we add the lengths of the inside and outside perimeters: 25 m + 31 m = 56 m.
Therefore, the correct answer is 56 m, not 36.22 m.
I apologize for any confusion caused. Let's go through the solution step by step to determine the correct length of wood needed for the forms.
1. Find the length of the inner perimeter:
The inner perimeter is equal to the perimeter of the triangular flower garden.
Perimeter = 10 m + 7 m + 8 m = 25 m
2. Find the length of the outer perimeter:
The outer perimeter is the sum of the inner perimeter and twice the width of the walking path on all sides.
Outer perimeter = Inner perimeter + 2 * (1 m + 1 m) = 25 m + 2 m = 27 m
3. Calculate the length of wood needed for the inside form:
As the inside form follows the shape of the inner perimeter, it will have the same length.
Length of wood for the inside form = 25 m
4. Calculate the length of wood needed for the outside form:
The outside form follows the shape of the outer perimeter, which includes the walking path.
To calculate the length of wood needed for the outside form, we will subtract the length of the inner form from the length of the outer form.
Length of wood for the outside form = Outer perimeter - Inner perimeter
Length of wood for the outside form = 27 m - 25 m = 2 m
5. Find the total length of wood needed for both forms:
The total length of wood needed is the sum of the lengths of the inside and outside forms.
Total length of wood = Length of wood for the inside form + Length of wood for the outside form
Total length of wood = 25 m + 2 m = 27 m
So, based on these steps, the correct total length of wood needed to build the forms is 27 meters, not 36.22 meters.
I apologize for any confusion or frustration. It seems that there might be a misunderstanding or error in the given solution. Let's go through the problem step by step to determine the total length of wood needed for the forms.
1. Start by calculating the perimeter of the triangular flower garden. The sides of the triangle are given as 10 m, 7 m, and 8 m. The perimeter is the sum of these side lengths: 10 + 7 + 8 = 25 m.
2. Since the border is to be a straight walking path 1 m wide on all sides of the garden, we need to determine the outer dimensions of the border. To do this, add 1 m to each side of the garden.
The new dimensions of the garden, considering the border, would be:
- The side opposite the 10 m side will now be 10 m + 2(1 m) = 12 m.
- The side opposite the 7 m side will now be 7 m + 2(1 m) = 9 m.
- The side opposite the 8 m side will now be 8 m + 2(1 m) = 10 m.
3. Calculate the perimeter of the outer dimensions of the border. The sum of the new side lengths will give us the length of wood needed for the forms.
Perimeter = 12 m + 9 m + 10 m = 31 m.
Therefore, based on these calculations, the total length of wood needed to build the forms would be 31 m, not 36.22 m as stated in the answer provided.