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Answer :
* Define the variables: Let $x$ be the length of the two equal sides and $y$ be the length of the shortest side.
* Write the perimeter equation: $x + x + y = 7.5$.
* Substitute the given value of $y$: $2x + 2.1 = 7.5$.
* The equation to find $x$ is: $\boxed{2.1+2 x=7.5}$.
### Explanation
1. Set up the equation for the perimeter
Let $x$ be the length of each of the two equal sides of the isosceles triangle, and let $y$ be the length of the shortest side. The perimeter of the triangle is the sum of the lengths of its sides, which is given as 7.5 m. Therefore, we have the equation $x + x + y = 7.5$. We are given that the shortest side $y$ measures 2.1 m. Substituting this value into the equation, we get $2x + 2.1 = 7.5$.
2. State the equation
The equation that can be used to find the value of $x$ is $2x + 2.1 = 7.5$.
### Examples
Understanding perimeters is useful in many real-world scenarios. For example, if you're building a fence around a yard, you need to know the perimeter to determine how much fencing material to buy. Similarly, if you're framing a picture, the perimeter of the picture determines the length of the frame you'll need. Knowing how to set up and solve equations for perimeters helps in these practical situations.
* Write the perimeter equation: $x + x + y = 7.5$.
* Substitute the given value of $y$: $2x + 2.1 = 7.5$.
* The equation to find $x$ is: $\boxed{2.1+2 x=7.5}$.
### Explanation
1. Set up the equation for the perimeter
Let $x$ be the length of each of the two equal sides of the isosceles triangle, and let $y$ be the length of the shortest side. The perimeter of the triangle is the sum of the lengths of its sides, which is given as 7.5 m. Therefore, we have the equation $x + x + y = 7.5$. We are given that the shortest side $y$ measures 2.1 m. Substituting this value into the equation, we get $2x + 2.1 = 7.5$.
2. State the equation
The equation that can be used to find the value of $x$ is $2x + 2.1 = 7.5$.
### Examples
Understanding perimeters is useful in many real-world scenarios. For example, if you're building a fence around a yard, you need to know the perimeter to determine how much fencing material to buy. Similarly, if you're framing a picture, the perimeter of the picture determines the length of the frame you'll need. Knowing how to set up and solve equations for perimeters helps in these practical situations.
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