Answer :
- The problem states that an isosceles triangle has a perimeter of 7.5 m and the shortest side, \(y\), measures 2.1 m.
- We represent the two equal sides of the isosceles triangle as \(x\).
- The perimeter equation is then expressed as \(2x + y = 7.5\).
- Substituting the value of \(y\), the equation becomes \(2x + 2.1 = 7.5\), which can be used to find the value of \(x\). The final answer is \(\boxed{2x + 2.1 = 7.5}\).
### Explanation
1. Analyze the problem
Let's analyze the given information. We have an isosceles triangle with a perimeter of 7.5 meters. One of the sides, which is the shortest side, measures 2.1 meters. We need to find an equation that can be used to find the length of the other two equal sides, which are represented by $x$.
2. Formulate the equation
Since the triangle is isosceles, it has two sides of equal length. Let's denote the length of these two sides as $x$. The perimeter of a triangle is the sum of the lengths of all its sides. In this case, the perimeter is given as 7.5 meters, and the shortest side is 2.1 meters. Therefore, we can write the equation for the perimeter as:$$x + x + 2.1 = 7.5$$
3. Simplify the equation
Combining the like terms, we get:$$2x + 2.1 = 7.5$$This equation relates the length of the equal sides ($x$) to the given perimeter (7.5 m) and the shortest side (2.1 m).
4. State the final equation
Therefore, the equation that can be used to find the value of $x$ is:$$2x + 2.1 = 7.5$$
### Examples
Understanding perimeters and setting up equations is crucial in many real-world scenarios. For instance, if you're building a fence around a triangular garden where two sides must be equal, and you know the total length of fencing you have, you can use this equation to determine the length of the equal sides. Similarly, if you are designing a clothing item that has triangular elements, knowing the perimeter and one side allows you to calculate the dimensions of the other sides, ensuring the design fits correctly.
- We represent the two equal sides of the isosceles triangle as \(x\).
- The perimeter equation is then expressed as \(2x + y = 7.5\).
- Substituting the value of \(y\), the equation becomes \(2x + 2.1 = 7.5\), which can be used to find the value of \(x\). The final answer is \(\boxed{2x + 2.1 = 7.5}\).
### Explanation
1. Analyze the problem
Let's analyze the given information. We have an isosceles triangle with a perimeter of 7.5 meters. One of the sides, which is the shortest side, measures 2.1 meters. We need to find an equation that can be used to find the length of the other two equal sides, which are represented by $x$.
2. Formulate the equation
Since the triangle is isosceles, it has two sides of equal length. Let's denote the length of these two sides as $x$. The perimeter of a triangle is the sum of the lengths of all its sides. In this case, the perimeter is given as 7.5 meters, and the shortest side is 2.1 meters. Therefore, we can write the equation for the perimeter as:$$x + x + 2.1 = 7.5$$
3. Simplify the equation
Combining the like terms, we get:$$2x + 2.1 = 7.5$$This equation relates the length of the equal sides ($x$) to the given perimeter (7.5 m) and the shortest side (2.1 m).
4. State the final equation
Therefore, the equation that can be used to find the value of $x$ is:$$2x + 2.1 = 7.5$$
### Examples
Understanding perimeters and setting up equations is crucial in many real-world scenarios. For instance, if you're building a fence around a triangular garden where two sides must be equal, and you know the total length of fencing you have, you can use this equation to determine the length of the equal sides. Similarly, if you are designing a clothing item that has triangular elements, knowing the perimeter and one side allows you to calculate the dimensions of the other sides, ensuring the design fits correctly.