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Make a table of length of the side of an equilateral triangle and its perimeter by taking four different lengths and draw the side-perimeter graph. From the graph, read the following
(1) perimeter, when the side is 2.5 units.
(ii) length of side, when perimeter is 10.5 units.?
(1) perimeter, when the side is 2.5 units.
(ii) length of side, when perimeter is 10.5 units.?
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Make a table of length of the side of an equilateral triangle and its ...
Here’s a detailed guide on the relationship between the side length of an equilateral triangle and its perimeter.
Table of Side Length and Perimeter
| Side Length (units) | Perimeter (units) |
|---------------------|-------------------|
| 1 | 3 |
| 2 | 6 |
| 3 | 9 |
| 4 | 12 |
Perimeter Calculation
The perimeter \( P \) of an equilateral triangle can be calculated using the formula:
\[ P = 3 \times \text{side length} \]
This means that for any given side length \( s \), the perimeter will always be three times that length.
Graphing the Relationship
To visualize the relationship, plot the side lengths on the x-axis and the corresponding perimeters on the y-axis. This will yield a straight line, indicating a linear relationship between side length and perimeter.
Reading the Graph
1. Perimeter when the side is 2.5 units:
- Using the formula:
\[ P = 3 \times 2.5 = 7.5 \text{ units} \]
- Thus, from the graph, when the side length is 2.5 units, the perimeter is 7.5 units.
2. Length of side when perimeter is 10.5 units:
- Rearranging the perimeter formula gives:
\[ \text{side length} = \frac{P}{3} \]
- For a perimeter of 10.5 units:
\[ \text{side length} = \frac{10.5}{3} = 3.5 \text{ units} \]
- Therefore, when the perimeter is 10.5 units, the side length is 3.5 units.
This analysis illustrates the straightforward relationship between the side length and perimeter of an equilateral triangle, making it easy to derive one from the other.
Table of Side Length and Perimeter
| Side Length (units) | Perimeter (units) |
|---------------------|-------------------|
| 1 | 3 |
| 2 | 6 |
| 3 | 9 |
| 4 | 12 |
Perimeter Calculation
The perimeter \( P \) of an equilateral triangle can be calculated using the formula:
\[ P = 3 \times \text{side length} \]
This means that for any given side length \( s \), the perimeter will always be three times that length.
Graphing the Relationship
To visualize the relationship, plot the side lengths on the x-axis and the corresponding perimeters on the y-axis. This will yield a straight line, indicating a linear relationship between side length and perimeter.
Reading the Graph
1. Perimeter when the side is 2.5 units:
- Using the formula:
\[ P = 3 \times 2.5 = 7.5 \text{ units} \]
- Thus, from the graph, when the side length is 2.5 units, the perimeter is 7.5 units.
2. Length of side when perimeter is 10.5 units:
- Rearranging the perimeter formula gives:
\[ \text{side length} = \frac{P}{3} \]
- For a perimeter of 10.5 units:
\[ \text{side length} = \frac{10.5}{3} = 3.5 \text{ units} \]
- Therefore, when the perimeter is 10.5 units, the side length is 3.5 units.
This analysis illustrates the straightforward relationship between the side length and perimeter of an equilateral triangle, making it easy to derive one from the other.
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Make a table of length of the side of an equilateral triangle and its perimeter by taking four different lengths and draw the side-perimeter graph. From the graph, read the following(1) perimeter, when the side is 2.5 units.(ii) length of side, when perimeter is 10.5 units.?
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Make a table of length of the side of an equilateral triangle and its perimeter by taking four different lengths and draw the side-perimeter graph. From the graph, read the following(1) perimeter, when the side is 2.5 units.(ii) length of side, when perimeter is 10.5 units.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Make a table of length of the side of an equilateral triangle and its perimeter by taking four different lengths and draw the side-perimeter graph. From the graph, read the following(1) perimeter, when the side is 2.5 units.(ii) length of side, when perimeter is 10.5 units.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Make a table of length of the side of an equilateral triangle and its perimeter by taking four different lengths and draw the side-perimeter graph. From the graph, read the following(1) perimeter, when the side is 2.5 units.(ii) length of side, when perimeter is 10.5 units.?.
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