Answer :
* The perimeter of the isosceles triangle is expressed as $2x + y = 7.5$.
* Substitute the value of the shortest side $y = 2.1$ into the perimeter equation: $2x + 2.1 = 7.5$.
* The equation to find the value of $x$ is $2x + 2.1 = 7.5$, which is equivalent to $2.1 + 2x = 7.5$.
* The correct equation is $\boxed{2.1 + 2x = 7.5}$.
### Explanation
1. Analyze the problem and form the equation.
Let's analyze the given information.
We have an isosceles triangle with two sides of equal length, denoted by $x$, and a third side of length $y$. The perimeter of the triangle is 7.5 m, and the shortest side, $y$, measures 2.1 m. We need to find the equation that can be used to find the value of $x$.
The perimeter of a triangle is the sum of the lengths of its three sides. In this case, the perimeter is given by:
$$x + x + y = 7.5$$
$$2x + y = 7.5$$
We are given that $y = 2.1$ m. Substituting this value into the equation, we get:
$$2x + 2.1 = 7.5$$
This is the equation we need to find the value of $x$.
2. Compare the equation with the given options.
Now, let's compare the equation we derived with the given options:
The equation we derived is:
$$2x + 2.1 = 7.5$$
Comparing this with the given options:
- $2x - 2.1 = 7.5$ (Incorrect)
- $4.2 + y = 7.5$ (Incorrect, as it doesn't involve $x$)
- $y - 4.2 = 7.5$ (Incorrect, as it doesn't involve $x$)
- $2.1 + 2x = 7.5$ (Correct, as it is the same as our derived equation)
3. State the final answer.
The correct equation is:
$$2.1 + 2x = 7.5$$
### Examples
Understanding perimeters and side lengths of triangles is crucial in various real-world applications. For instance, architects use these concepts to design buildings with specific structural requirements. Similarly, landscapers use them to plan gardens and outdoor spaces, ensuring accurate dimensions and aesthetically pleasing layouts. In construction, knowing the perimeter helps in estimating the amount of fencing or edging needed for a plot of land.
* Substitute the value of the shortest side $y = 2.1$ into the perimeter equation: $2x + 2.1 = 7.5$.
* The equation to find the value of $x$ is $2x + 2.1 = 7.5$, which is equivalent to $2.1 + 2x = 7.5$.
* The correct equation is $\boxed{2.1 + 2x = 7.5}$.
### Explanation
1. Analyze the problem and form the equation.
Let's analyze the given information.
We have an isosceles triangle with two sides of equal length, denoted by $x$, and a third side of length $y$. The perimeter of the triangle is 7.5 m, and the shortest side, $y$, measures 2.1 m. We need to find the equation that can be used to find the value of $x$.
The perimeter of a triangle is the sum of the lengths of its three sides. In this case, the perimeter is given by:
$$x + x + y = 7.5$$
$$2x + y = 7.5$$
We are given that $y = 2.1$ m. Substituting this value into the equation, we get:
$$2x + 2.1 = 7.5$$
This is the equation we need to find the value of $x$.
2. Compare the equation with the given options.
Now, let's compare the equation we derived with the given options:
The equation we derived is:
$$2x + 2.1 = 7.5$$
Comparing this with the given options:
- $2x - 2.1 = 7.5$ (Incorrect)
- $4.2 + y = 7.5$ (Incorrect, as it doesn't involve $x$)
- $y - 4.2 = 7.5$ (Incorrect, as it doesn't involve $x$)
- $2.1 + 2x = 7.5$ (Correct, as it is the same as our derived equation)
3. State the final answer.
The correct equation is:
$$2.1 + 2x = 7.5$$
### Examples
Understanding perimeters and side lengths of triangles is crucial in various real-world applications. For instance, architects use these concepts to design buildings with specific structural requirements. Similarly, landscapers use them to plan gardens and outdoor spaces, ensuring accurate dimensions and aesthetically pleasing layouts. In construction, knowing the perimeter helps in estimating the amount of fencing or edging needed for a plot of land.