Answer :
To find the value of [tex]\( x \)[/tex] for the given isosceles triangle, we need to set up an equation based on the information provided:
1. Understanding the Triangle:
- An isosceles triangle has two equal sides and a different third side.
- We are given the perimeter of the triangle is 7.5 meters.
- The shortest side (third side) measures 2.1 meters.
2. Set Up the Equation:
- The perimeter of a triangle is the sum of all its sides.
- In an isosceles triangle, if the shortest side is [tex]\( y = 2.1 \)[/tex], then the two equal sides can be represented as [tex]\( x \)[/tex] each.
3. Equation for Perimeter:
[tex]\[
\text{Perimeter} = x + x + 2.1 = 7.5
\][/tex]
Simplified, it becomes:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
4. Identify the Correct Equation:
From the options given:
- [tex]\( 2x - 2.1 = 7.5 \)[/tex]
- [tex]\( 4.2 + y = 7.5 \)[/tex]
- [tex]\( y - 4.2 = 7.5 \)[/tex]
- [tex]\( 2.1 + 2x = 7.5 \)[/tex]
The correct equation that matches our setup is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
This equation can be used to find the value of [tex]\( x \)[/tex].
1. Understanding the Triangle:
- An isosceles triangle has two equal sides and a different third side.
- We are given the perimeter of the triangle is 7.5 meters.
- The shortest side (third side) measures 2.1 meters.
2. Set Up the Equation:
- The perimeter of a triangle is the sum of all its sides.
- In an isosceles triangle, if the shortest side is [tex]\( y = 2.1 \)[/tex], then the two equal sides can be represented as [tex]\( x \)[/tex] each.
3. Equation for Perimeter:
[tex]\[
\text{Perimeter} = x + x + 2.1 = 7.5
\][/tex]
Simplified, it becomes:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
4. Identify the Correct Equation:
From the options given:
- [tex]\( 2x - 2.1 = 7.5 \)[/tex]
- [tex]\( 4.2 + y = 7.5 \)[/tex]
- [tex]\( y - 4.2 = 7.5 \)[/tex]
- [tex]\( 2.1 + 2x = 7.5 \)[/tex]
The correct equation that matches our setup is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
This equation can be used to find the value of [tex]\( x \)[/tex].
