Answer :
To solve this problem, we need to determine which equation can be used to find the value of [tex]\( x \)[/tex] in an isosceles triangle given:
- The perimeter of the triangle is 7.5 meters.
- The shortest side [tex]\( y \)[/tex] is 2.1 meters.
In an isosceles triangle, two sides are of equal length, and the third side is different. For this problem, we'll assume the third side is the shortest side, [tex]\( y = 2.1 \)[/tex] meters.
Given these values, the perimeter of the triangle is calculated as:
[tex]\[ \text{Perimeter} = \text{side}_1 + \text{side}_2 + \text{side}_3 \][/tex]
Since two sides are equal in an isosceles triangle, we can say:
[tex]\[ \text{Perimeter} = 2x + y \][/tex]
We know:
- The perimeter is 7.5 meters.
- [tex]\( y = 2.1 \)[/tex] meters.
Plug these values into the equation:
[tex]\[ 7.5 = 2x + 2.1 \][/tex]
We need to isolate [tex]\( x \)[/tex] to find the correct equation:
1. Start by setting up the equation for the perimeter:
[tex]\[ 7.5 = 2x + 2.1 \][/tex]
2. Subtract 2.1 from both sides to isolate the terms involving [tex]\( x \)[/tex]:
[tex]\[ 7.5 - 2.1 = 2x \][/tex]
3. Simplify the left side:
[tex]\[ 5.4 = 2x \][/tex]
4. This equation can be rewritten as:
[tex]\[ 2x - 5.4 = 0 \][/tex]
Based on the given options, the equation [tex]\( 2x - 7.5 = 0 \)[/tex] with sides [tex]\( 2.1 + 2x = 7.5 \)[/tex] simplifies correctly to [tex]\( 2x - 5.4 = 0 \)[/tex], which effectively describes finding [tex]\( x \)[/tex] in the isosceles triangle.
Thus, the correct option indicating how to find [tex]\( x \)[/tex] is related to these simplified values, which was:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
- The perimeter of the triangle is 7.5 meters.
- The shortest side [tex]\( y \)[/tex] is 2.1 meters.
In an isosceles triangle, two sides are of equal length, and the third side is different. For this problem, we'll assume the third side is the shortest side, [tex]\( y = 2.1 \)[/tex] meters.
Given these values, the perimeter of the triangle is calculated as:
[tex]\[ \text{Perimeter} = \text{side}_1 + \text{side}_2 + \text{side}_3 \][/tex]
Since two sides are equal in an isosceles triangle, we can say:
[tex]\[ \text{Perimeter} = 2x + y \][/tex]
We know:
- The perimeter is 7.5 meters.
- [tex]\( y = 2.1 \)[/tex] meters.
Plug these values into the equation:
[tex]\[ 7.5 = 2x + 2.1 \][/tex]
We need to isolate [tex]\( x \)[/tex] to find the correct equation:
1. Start by setting up the equation for the perimeter:
[tex]\[ 7.5 = 2x + 2.1 \][/tex]
2. Subtract 2.1 from both sides to isolate the terms involving [tex]\( x \)[/tex]:
[tex]\[ 7.5 - 2.1 = 2x \][/tex]
3. Simplify the left side:
[tex]\[ 5.4 = 2x \][/tex]
4. This equation can be rewritten as:
[tex]\[ 2x - 5.4 = 0 \][/tex]
Based on the given options, the equation [tex]\( 2x - 7.5 = 0 \)[/tex] with sides [tex]\( 2.1 + 2x = 7.5 \)[/tex] simplifies correctly to [tex]\( 2x - 5.4 = 0 \)[/tex], which effectively describes finding [tex]\( x \)[/tex] in the isosceles triangle.
Thus, the correct option indicating how to find [tex]\( x \)[/tex] is related to these simplified values, which was:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
