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Answer :
To solve this problem, we need to determine if any of the given equations correctly represent the conditions of the isosceles triangle's perimeter and side lengths.
### Understanding the Problem:
We have an isosceles triangle with:
- A perimeter of 7.5 meters.
- The shortest side, [tex]\( y \)[/tex], measuring 21 meters.
In an isosceles triangle, if one side is the shortest, the other two sides are equal. Hence, the equation for the perimeter could be expressed as:
[tex]\[ 2x + y = \text{perimeter} \][/tex]
Substituting the values we know:
[tex]\[ 2x + 21 = 7.5 \][/tex]
### Checking the Equations:
Let's check each given choice:
1. [tex]\(2x - 2.1 = 7.5\)[/tex]:
- This would imply that [tex]\(2x = 9.6\)[/tex], which doesn't match our setup as [tex]\(2x\)[/tex] should be calculated from our equation above.
2. [tex]\(4.2 + 1.7 = 0.5\)[/tex]:
- This equation does not make sense in the context of calculating [tex]\(x\)[/tex] or the perimeter directly.
3. [tex]\(y - 4.2 = 7.5\)[/tex]:
- This simplifies to [tex]\(y = 11.7\)[/tex], which contradicts the given side length [tex]\(y = 21\)[/tex].
4. [tex]\(2.1 + 2x = 7.5\)[/tex]:
- Rearranging this equation yields:
- [tex]\(2x = 7.5 - 2.1\)[/tex]
- [tex]\(2x = 5.4\)[/tex]
None of these equations can provide a logical measure for the triangle, especially when the side [tex]\( y \)[/tex] is reported as 21 m, which exceeds the stated perimeter of 7.5 m.
### Conclusion:
The given conditions create a contradiction, since a perimeter of 7.5 m is less than the known length of side [tex]\( y = 21 \)[/tex] m, which is not possible for a valid triangle. Thus, none of the provided equations correctly describe this scenario with the given measurements.
### Understanding the Problem:
We have an isosceles triangle with:
- A perimeter of 7.5 meters.
- The shortest side, [tex]\( y \)[/tex], measuring 21 meters.
In an isosceles triangle, if one side is the shortest, the other two sides are equal. Hence, the equation for the perimeter could be expressed as:
[tex]\[ 2x + y = \text{perimeter} \][/tex]
Substituting the values we know:
[tex]\[ 2x + 21 = 7.5 \][/tex]
### Checking the Equations:
Let's check each given choice:
1. [tex]\(2x - 2.1 = 7.5\)[/tex]:
- This would imply that [tex]\(2x = 9.6\)[/tex], which doesn't match our setup as [tex]\(2x\)[/tex] should be calculated from our equation above.
2. [tex]\(4.2 + 1.7 = 0.5\)[/tex]:
- This equation does not make sense in the context of calculating [tex]\(x\)[/tex] or the perimeter directly.
3. [tex]\(y - 4.2 = 7.5\)[/tex]:
- This simplifies to [tex]\(y = 11.7\)[/tex], which contradicts the given side length [tex]\(y = 21\)[/tex].
4. [tex]\(2.1 + 2x = 7.5\)[/tex]:
- Rearranging this equation yields:
- [tex]\(2x = 7.5 - 2.1\)[/tex]
- [tex]\(2x = 5.4\)[/tex]
None of these equations can provide a logical measure for the triangle, especially when the side [tex]\( y \)[/tex] is reported as 21 m, which exceeds the stated perimeter of 7.5 m.
### Conclusion:
The given conditions create a contradiction, since a perimeter of 7.5 m is less than the known length of side [tex]\( y = 21 \)[/tex] m, which is not possible for a valid triangle. Thus, none of the provided equations correctly describe this scenario with the given measurements.
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