Question
A rectangular garden measures 15 meters by 8 meters. If a path that is 1 meter wide is built around the garden, what is the area of the path?
Answers
GPT-4o mini
To find the area of the path around the garden, we first need to determine the dimensions of the garden including the path.
The original dimensions of the garden are:
- Length = 15 meters
- Width = 8 meters
When a path that is 1 meter wide is built around the garden, we need to add 2 meters to each dimension (1 meter for each side of the garden).
The new dimensions will be:
- New Length = 15 meters + 2 × 1 meter = 15 meters + 2 meters = 17 meters
- New Width = 8 meters + 2 × 1 meter = 8 meters + 2 meters = 10 meters
Next, we can calculate the area of the larger rectangle (garden plus path) and the area of the original garden.
1. Area of the larger rectangle (garden plus path):
\[
\text{Area}_{\text{larger}} = \text{Length} \times \text{Width} = 17 \, \text{meters} \times 10 \, \text{meters} = 170 \, \text{square meters}
\]
2. Area of the original garden:
\[
\text{Area}_{\text{garden}} = \text{Length} \times \text{Width} = 15 \, \text{meters} \times 8 \, \text{meters} = 120 \, \text{square meters}
\]
Now, to find the area of the path, we subtract the area of the garden from the area of the larger rectangle:
\[
\text{Area}_{\text{path}} = \text{Area}_{\text{larger}} - \text{Area}_{\text{garden}} = 170 \, \text{square meters} - 120 \, \text{square meters} = 50 \, \text{square meters}
\]
Thus, the area of the path is \(\boxed{50}\) square meters.
The original dimensions of the garden are:
- Length = 15 meters
- Width = 8 meters
When a path that is 1 meter wide is built around the garden, we need to add 2 meters to each dimension (1 meter for each side of the garden).
The new dimensions will be:
- New Length = 15 meters + 2 × 1 meter = 15 meters + 2 meters = 17 meters
- New Width = 8 meters + 2 × 1 meter = 8 meters + 2 meters = 10 meters
Next, we can calculate the area of the larger rectangle (garden plus path) and the area of the original garden.
1. Area of the larger rectangle (garden plus path):
\[
\text{Area}_{\text{larger}} = \text{Length} \times \text{Width} = 17 \, \text{meters} \times 10 \, \text{meters} = 170 \, \text{square meters}
\]
2. Area of the original garden:
\[
\text{Area}_{\text{garden}} = \text{Length} \times \text{Width} = 15 \, \text{meters} \times 8 \, \text{meters} = 120 \, \text{square meters}
\]
Now, to find the area of the path, we subtract the area of the garden from the area of the larger rectangle:
\[
\text{Area}_{\text{path}} = \text{Area}_{\text{larger}} - \text{Area}_{\text{garden}} = 170 \, \text{square meters} - 120 \, \text{square meters} = 50 \, \text{square meters}
\]
Thus, the area of the path is \(\boxed{50}\) square meters.