Answer :
- We have an isosceles triangle with two equal sides $x$ and a shortest side $y = 2.1$ m.
- The perimeter of the triangle is 7.5 m, so $x + x + y = 7.5$.
- Substitute $y = 2.1$ m into the equation: $2x + 2.1 = 7.5$.
- The equation to find $x$ is: $\boxed{2.1+2 x=7.5}$.
### Explanation
1. Analyze the problem
Let's analyze the given information. We have an isosceles triangle with two sides of equal length, denoted as $x$, and a third side, $y$, which is the shortest side with a length of 2.1 m. The perimeter of the triangle is 7.5 m. The perimeter is the sum of all sides, so we can write the equation: $x + x + y = 7.5$.
2. Substitute the value of y
Now, substitute the value of $y$ into the equation. We know that $y = 2.1$ m, so the equation becomes: $2x + 2.1 = 7.5$. This equation can be used to find the value of $x$.
3. State the equation
The equation that can be used to find the value of $x$ is $2x + 2.1 = 7.5$.
### Examples
Understanding perimeters and side lengths of triangles is useful in many real-world scenarios. For example, if you are building a triangular garden bed and know the length of one side and the total perimeter, you can use this equation to determine the length of the other two equal sides. This ensures you have the correct dimensions for your garden design.
- The perimeter of the triangle is 7.5 m, so $x + x + y = 7.5$.
- Substitute $y = 2.1$ m into the equation: $2x + 2.1 = 7.5$.
- The equation to find $x$ is: $\boxed{2.1+2 x=7.5}$.
### Explanation
1. Analyze the problem
Let's analyze the given information. We have an isosceles triangle with two sides of equal length, denoted as $x$, and a third side, $y$, which is the shortest side with a length of 2.1 m. The perimeter of the triangle is 7.5 m. The perimeter is the sum of all sides, so we can write the equation: $x + x + y = 7.5$.
2. Substitute the value of y
Now, substitute the value of $y$ into the equation. We know that $y = 2.1$ m, so the equation becomes: $2x + 2.1 = 7.5$. This equation can be used to find the value of $x$.
3. State the equation
The equation that can be used to find the value of $x$ is $2x + 2.1 = 7.5$.
### Examples
Understanding perimeters and side lengths of triangles is useful in many real-world scenarios. For example, if you are building a triangular garden bed and know the length of one side and the total perimeter, you can use this equation to determine the length of the other two equal sides. This ensures you have the correct dimensions for your garden design.