Answer :
Sure! Let's solve the problem step by step.
We're given an isosceles triangle with a perimeter of 7.5 meters. We know one side, the shortest side, is 2.1 meters long. In an isosceles triangle, two sides are of equal length, and we're asked to find the value of [tex]\( x \)[/tex], which represents this equal length.
Here's how we can approach the problem:
1. Identify the components:
- The shortest side [tex]\( y = 2.1 \, \text{m} \)[/tex].
- The perimeter of the triangle is [tex]\( 7.5 \, \text{m} \)[/tex].
- The other two sides are equal, so let's denote each of these sides as [tex]\( x \)[/tex].
2. Write an equation for the perimeter:
- The perimeter of an isosceles triangle can be expressed as the sum of its three sides:
[tex]\[
x + x + y = \text{Perimeter}
\][/tex]
- Substituting the given values, we have:
[tex]\[
x + x + 2.1 = 7.5
\][/tex]
3. Simplify the equation:
- Combine the [tex]\( x \)[/tex] terms:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
4. Choose the correct equation:
- The equation [tex]\( 2x + 2.1 = 7.5 \)[/tex] is one of the options provided. It accurately represents the scenario given in the problem.
This equation allows us to solve for [tex]\( x \)[/tex], which represents the length of the two equal sides of the isosceles triangle.
We're given an isosceles triangle with a perimeter of 7.5 meters. We know one side, the shortest side, is 2.1 meters long. In an isosceles triangle, two sides are of equal length, and we're asked to find the value of [tex]\( x \)[/tex], which represents this equal length.
Here's how we can approach the problem:
1. Identify the components:
- The shortest side [tex]\( y = 2.1 \, \text{m} \)[/tex].
- The perimeter of the triangle is [tex]\( 7.5 \, \text{m} \)[/tex].
- The other two sides are equal, so let's denote each of these sides as [tex]\( x \)[/tex].
2. Write an equation for the perimeter:
- The perimeter of an isosceles triangle can be expressed as the sum of its three sides:
[tex]\[
x + x + y = \text{Perimeter}
\][/tex]
- Substituting the given values, we have:
[tex]\[
x + x + 2.1 = 7.5
\][/tex]
3. Simplify the equation:
- Combine the [tex]\( x \)[/tex] terms:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
4. Choose the correct equation:
- The equation [tex]\( 2x + 2.1 = 7.5 \)[/tex] is one of the options provided. It accurately represents the scenario given in the problem.
This equation allows us to solve for [tex]\( x \)[/tex], which represents the length of the two equal sides of the isosceles triangle.
