Answer :
- The problem involves an isosceles triangle with a given perimeter and one side length.
- The goal is to find the equation that relates the unknown side length $x$ to the given perimeter and side length $y$.
- The perimeter of the triangle is expressed as $2x + y = 7.5$.
- The correct equation is identified as $\boxed{2.1 + 2x = 7.5}$.
### Explanation
1. Problem Analysis
Let's analyze the given information.
We have an isosceles triangle with a perimeter of 7.5 m. One side, denoted as $y$, is 2.1 m. We need to find an equation to determine the value of $x$, which represents the length of the other two equal sides.
The perimeter of a triangle is the sum of its sides. In this case, the perimeter is $x + x + y = 2x + y$. We know the perimeter is 7.5 m and $y = 2.1$ m. So, we can write the equation as $2x + 2.1 = 7.5$.
2. Finding the Correct Equation
Now, let's find the correct equation from the given options:
1. $2x - 2.1 = 7.5$ (Incorrect, it should be addition, not subtraction)
2. $4.2 + y = 7.5$ (Incorrect, it should include $x$ to find its value)
3. $y - 4.2 = 7.5$ (Incorrect, this doesn't relate to the perimeter or $x$)
4. $2.1 + 2x = 7.5$ (Correct, this is the same as $2x + 2.1 = 7.5$)
So, the correct equation is $2.1 + 2x = 7.5$.
3. Final Answer
The equation that can be used to find the value of $x$ is $2.1 + 2x = 7.5$.
### Examples
Understanding perimeters is crucial in many real-world scenarios. For instance, when fencing a garden, you need to calculate the perimeter to determine the amount of fencing material required. Similarly, when framing a picture or creating a border around a room, knowing the perimeter helps in accurately estimating the materials needed, saving both time and resources.
- The goal is to find the equation that relates the unknown side length $x$ to the given perimeter and side length $y$.
- The perimeter of the triangle is expressed as $2x + y = 7.5$.
- The correct equation is identified as $\boxed{2.1 + 2x = 7.5}$.
### Explanation
1. Problem Analysis
Let's analyze the given information.
We have an isosceles triangle with a perimeter of 7.5 m. One side, denoted as $y$, is 2.1 m. We need to find an equation to determine the value of $x$, which represents the length of the other two equal sides.
The perimeter of a triangle is the sum of its sides. In this case, the perimeter is $x + x + y = 2x + y$. We know the perimeter is 7.5 m and $y = 2.1$ m. So, we can write the equation as $2x + 2.1 = 7.5$.
2. Finding the Correct Equation
Now, let's find the correct equation from the given options:
1. $2x - 2.1 = 7.5$ (Incorrect, it should be addition, not subtraction)
2. $4.2 + y = 7.5$ (Incorrect, it should include $x$ to find its value)
3. $y - 4.2 = 7.5$ (Incorrect, this doesn't relate to the perimeter or $x$)
4. $2.1 + 2x = 7.5$ (Correct, this is the same as $2x + 2.1 = 7.5$)
So, the correct equation is $2.1 + 2x = 7.5$.
3. Final Answer
The equation that can be used to find the value of $x$ is $2.1 + 2x = 7.5$.
### Examples
Understanding perimeters is crucial in many real-world scenarios. For instance, when fencing a garden, you need to calculate the perimeter to determine the amount of fencing material required. Similarly, when framing a picture or creating a border around a room, knowing the perimeter helps in accurately estimating the materials needed, saving both time and resources.