Answer :
* The perimeter of the isosceles triangle is expressed as the sum of its sides: $x + x + y = 7.5$.
* The equation simplifies to $2x + y = 7.5$.
* Substituting the given value of $y = 2.1$ m into the equation gives $2x + 2.1 = 7.5$.
* The equation to find the value of $x$ is therefore $\boxed{2.1 + 2x = 7.5}$.
### Explanation
1. Analyze the problem
Let's analyze the given information. We have an isosceles triangle with two sides of equal length, which we'll call $x$. The shortest side, $y$, is given as 2.1 m. The perimeter of the triangle is 7.5 m. Our goal is to find the equation that can be used to find the value of $x$.
2. Write the perimeter equation
The perimeter of any triangle is the sum of the lengths of its three sides. In this case, since we have an isosceles triangle, the perimeter is given by:
$$x + x + y = 7.5$$
Simplifying this, we get:
$$2x + y = 7.5$$
3. Substitute the value of y
We are given that the shortest side, $y$, is 2.1 m. Substitute this value into the equation:
$$2x + 2.1 = 7.5$$
4. State the final equation
Therefore, the equation that can be used to find the value of $x$ is:
$$2.1 + 2x = 7.5$$
### Examples
Understanding perimeters and side lengths of triangles is useful in many real-world scenarios. For example, if you're 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 sides, ensuring your garden bed is symmetrical and fits your space perfectly. This also applies to designing triangular structures or calculating distances in triangular layouts.
* The equation simplifies to $2x + y = 7.5$.
* Substituting the given value of $y = 2.1$ m into the equation gives $2x + 2.1 = 7.5$.
* The equation to find the value of $x$ is therefore $\boxed{2.1 + 2x = 7.5}$.
### Explanation
1. Analyze the problem
Let's analyze the given information. We have an isosceles triangle with two sides of equal length, which we'll call $x$. The shortest side, $y$, is given as 2.1 m. The perimeter of the triangle is 7.5 m. Our goal is to find the equation that can be used to find the value of $x$.
2. Write the perimeter equation
The perimeter of any triangle is the sum of the lengths of its three sides. In this case, since we have an isosceles triangle, the perimeter is given by:
$$x + x + y = 7.5$$
Simplifying this, we get:
$$2x + y = 7.5$$
3. Substitute the value of y
We are given that the shortest side, $y$, is 2.1 m. Substitute this value into the equation:
$$2x + 2.1 = 7.5$$
4. State the final equation
Therefore, the equation that can be used to find the value of $x$ is:
$$2.1 + 2x = 7.5$$
### Examples
Understanding perimeters and side lengths of triangles is useful in many real-world scenarios. For example, if you're 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 sides, ensuring your garden bed is symmetrical and fits your space perfectly. This also applies to designing triangular structures or calculating distances in triangular layouts.