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Answer :
To solve the problem of finding the equation that can be used to determine the value of [tex]\(x\)[/tex] in the isosceles triangle, let's break down the components:
1. Identify the given information:
- The perimeter of the isosceles triangle is 7.5 meters.
- The shortest side, denoted as [tex]\(y\)[/tex], measures 2.1 meters.
2. Understand the properties of an isosceles triangle:
- In an isosceles triangle, two sides are of equal length, and the third side is different. Here, we'll assume the two equal sides are [tex]\(x\)[/tex].
3. Set up the equation for the perimeter:
- The perimeter of a triangle is the sum of the lengths of all its sides.
- For this triangle, the perimeter can be expressed as: [tex]\(2x + y = 7.5\)[/tex]
4. Substitute the known value of [tex]\(y\)[/tex]:
- We know the value of [tex]\(y\)[/tex] is 2.1 meters, so substitute it into the equation:
[tex]\(2x + 2.1 = 7.5\)[/tex]
5. Identify the correct equation from the options:
- The correct equation to find the value of [tex]\(x\)[/tex] is:
[tex]\(2.1 + 2x = 7.5\)[/tex]
Therefore, the equation that can be used to find the value of [tex]\(x\)[/tex] is [tex]\(2.1 + 2x = 7.5\)[/tex].
1. Identify the given information:
- The perimeter of the isosceles triangle is 7.5 meters.
- The shortest side, denoted as [tex]\(y\)[/tex], measures 2.1 meters.
2. Understand the properties of an isosceles triangle:
- In an isosceles triangle, two sides are of equal length, and the third side is different. Here, we'll assume the two equal sides are [tex]\(x\)[/tex].
3. Set up the equation for the perimeter:
- The perimeter of a triangle is the sum of the lengths of all its sides.
- For this triangle, the perimeter can be expressed as: [tex]\(2x + y = 7.5\)[/tex]
4. Substitute the known value of [tex]\(y\)[/tex]:
- We know the value of [tex]\(y\)[/tex] is 2.1 meters, so substitute it into the equation:
[tex]\(2x + 2.1 = 7.5\)[/tex]
5. Identify the correct equation from the options:
- The correct equation to find the value of [tex]\(x\)[/tex] is:
[tex]\(2.1 + 2x = 7.5\)[/tex]
Therefore, the equation that can be used to find the value of [tex]\(x\)[/tex] is [tex]\(2.1 + 2x = 7.5\)[/tex].
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