Answer :
To find the equation that can be used to determine the value of [tex]\( x \)[/tex] in an isosceles triangle with a perimeter of 7.5 meters and the shortest side [tex]\( y \)[/tex] measuring 2.1 meters, follow these steps:
1. Understand the properties of the isosceles triangle:
- In an isosceles triangle, two sides are of equal length. Let's denote each of these equal sides by [tex]\( x \)[/tex].
- The third side is given as [tex]\( y \)[/tex] and measures 2.1 meters.
2. Write the equation for the perimeter:
- The perimeter of a triangle is the sum of the lengths of all its sides.
- Therefore, the perimeter of this isosceles triangle can be written as:
[tex]\[
\text{Perimeter} = x + x + y
\][/tex]
- Simplify this to:
[tex]\[
\text{Perimeter} = 2x + y
\][/tex]
3. Substitute the given values:
- The given perimeter is 7.5 meters.
- The shortest side [tex]\( y \)[/tex] is 2.1 meters.
- Substitute these values into the equation:
[tex]\[
7.5 = 2x + 2.1
\][/tex]
4. Rearrange to form the equation:
- Bring the terms involving [tex]\( x \)[/tex] to one side:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
Therefore, the equation that can be used to find the value of [tex]\( x \)[/tex] given the shortest side of the isosceles triangle and the total perimeter is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
This matches with the fourth option provided:
[tex]\[
2.1 + 2 x = 7.5
\][/tex]
1. Understand the properties of the isosceles triangle:
- In an isosceles triangle, two sides are of equal length. Let's denote each of these equal sides by [tex]\( x \)[/tex].
- The third side is given as [tex]\( y \)[/tex] and measures 2.1 meters.
2. Write the equation for the perimeter:
- The perimeter of a triangle is the sum of the lengths of all its sides.
- Therefore, the perimeter of this isosceles triangle can be written as:
[tex]\[
\text{Perimeter} = x + x + y
\][/tex]
- Simplify this to:
[tex]\[
\text{Perimeter} = 2x + y
\][/tex]
3. Substitute the given values:
- The given perimeter is 7.5 meters.
- The shortest side [tex]\( y \)[/tex] is 2.1 meters.
- Substitute these values into the equation:
[tex]\[
7.5 = 2x + 2.1
\][/tex]
4. Rearrange to form the equation:
- Bring the terms involving [tex]\( x \)[/tex] to one side:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
Therefore, the equation that can be used to find the value of [tex]\( x \)[/tex] given the shortest side of the isosceles triangle and the total perimeter is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
This matches with the fourth option provided:
[tex]\[
2.1 + 2 x = 7.5
\][/tex]
