Answer :
* The perimeter of an isosceles triangle is the sum of its three sides, where two sides are equal.
* Represent the length of the two equal sides as $x$ and the shortest side as $y$, so the perimeter equation is $x + x + y = 7.5$.
* Simplify the equation to $2x + y = 7.5$.
* Substitute the given value of $y = 2.1$ m into the equation, resulting in the final equation: $\boxed{2.1 + 2x = 7.5}$.
### Explanation
1. Analyze the problem
Let's analyze the given information. We have an isosceles triangle with a perimeter of 7.5 m. One side, denoted as 'y', is the shortest side and measures 2.1 m. The other two sides are equal in length, and we'll call their length 'x'. Our goal is to find the equation that relates x and y to the perimeter.
2. Write the perimeter equation
The perimeter of any triangle is the sum of the lengths of its three sides. In this case, the perimeter is given by:
$x + x + y = 7.5$
Since the triangle is isosceles, two sides have the same length 'x'.
3. Substitute the value of y
Now, let's simplify the equation:
$2x + y = 7.5$
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
The equation that can be used to find the value of x is:
$2x + 2.1 = 7.5$
### Examples
Understanding perimeters is crucial in many real-world applications. For instance, when fencing a garden, you need to calculate the perimeter to determine the amount of fencing material required. Similarly, when framing a picture or creating a border for a craft project, knowing the perimeter helps you accurately measure and cut the materials. This concept extends to larger scales, such as city planning, where calculating the perimeters of blocks or parks is essential for efficient design and resource allocation.
* Represent the length of the two equal sides as $x$ and the shortest side as $y$, so the perimeter equation is $x + x + y = 7.5$.
* Simplify the equation to $2x + y = 7.5$.
* Substitute the given value of $y = 2.1$ m into the equation, resulting in the final equation: $\boxed{2.1 + 2x = 7.5}$.
### Explanation
1. Analyze the problem
Let's analyze the given information. We have an isosceles triangle with a perimeter of 7.5 m. One side, denoted as 'y', is the shortest side and measures 2.1 m. The other two sides are equal in length, and we'll call their length 'x'. Our goal is to find the equation that relates x and y to the perimeter.
2. Write the perimeter equation
The perimeter of any triangle is the sum of the lengths of its three sides. In this case, the perimeter is given by:
$x + x + y = 7.5$
Since the triangle is isosceles, two sides have the same length 'x'.
3. Substitute the value of y
Now, let's simplify the equation:
$2x + y = 7.5$
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
The equation that can be used to find the value of x is:
$2x + 2.1 = 7.5$
### Examples
Understanding perimeters is crucial in many real-world applications. For instance, when fencing a garden, you need to calculate the perimeter to determine the amount of fencing material required. Similarly, when framing a picture or creating a border for a craft project, knowing the perimeter helps you accurately measure and cut the materials. This concept extends to larger scales, such as city planning, where calculating the perimeters of blocks or parks is essential for efficient design and resource allocation.