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Answer :
To solve this problem and find the correct equation to determine the value of [tex]\( x \)[/tex], let's first identify the details of the isosceles triangle:
1. Perimeter of the Triangle: The perimeter is given as 7.5 meters.
2. Shortest Side: The shortest side, denoted as [tex]\( y \)[/tex], measures 2.1 meters.
3. Isosceles Triangle: In an isosceles triangle, two sides are equal in length. Let's represent the equal sides as [tex]\( x \)[/tex].
Since it's an isosceles triangle, the perimeter is made up by adding the three sides together:
- Two equal sides (each of length [tex]\( x \)[/tex]).
- The shortest side ([tex]\( y = 2.1 \)[/tex] meters).
The equation for the perimeter is:
[tex]\[ x + x + y = 7.5 \][/tex]
Simplifying this, we have:
[tex]\[ 2x + 2.1 = 7.5 \][/tex]
This fits with one of the given options: [tex]\( 2.1 + 2x = 7.5 \)[/tex].
Therefore, the equation to find the value of [tex]\( x \)[/tex] is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
This equation ensures that the sum of the lengths of all sides meets the given perimeter requirement of the triangle.
1. Perimeter of the Triangle: The perimeter is given as 7.5 meters.
2. Shortest Side: The shortest side, denoted as [tex]\( y \)[/tex], measures 2.1 meters.
3. Isosceles Triangle: In an isosceles triangle, two sides are equal in length. Let's represent the equal sides as [tex]\( x \)[/tex].
Since it's an isosceles triangle, the perimeter is made up by adding the three sides together:
- Two equal sides (each of length [tex]\( x \)[/tex]).
- The shortest side ([tex]\( y = 2.1 \)[/tex] meters).
The equation for the perimeter is:
[tex]\[ x + x + y = 7.5 \][/tex]
Simplifying this, we have:
[tex]\[ 2x + 2.1 = 7.5 \][/tex]
This fits with one of the given options: [tex]\( 2.1 + 2x = 7.5 \)[/tex].
Therefore, the equation to find the value of [tex]\( x \)[/tex] is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
This equation ensures that the sum of the lengths of all sides meets the given perimeter requirement of the triangle.
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