Answer :
To solve the problem, we need to find the appropriate equation that can be used to determine the value of [tex]\( x \)[/tex] given the conditions of the isosceles triangle.
Here's how to approach the problem step-by-step:
1. Understand the Properties of an Isosceles Triangle:
- An isosceles triangle has two sides that are equal.
- If we denote the equal sides by [tex]\( x \)[/tex] and the base or shortest side by [tex]\( y \)[/tex], then in this case, the shortest side [tex]\( y \)[/tex] is given as 2.1 meters.
2. Use the Perimeter Formula:
- The perimeter of a triangle is the sum of the lengths of all its sides.
- For an isosceles triangle with equal sides [tex]\( x \)[/tex], the perimeter equation would be:
[tex]\[
\text{Perimeter} = x + x + y
\][/tex]
- This simplifies to:
[tex]\[
\text{Perimeter} = 2x + y
\][/tex]
3. Substitute the Known Values:
- The perimeter is given as 7.5 meters, and the shortest side [tex]\( y \)[/tex] is 2.1 meters.
- Substitute these values into the perimeter equation:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
4. Select the Correct Equation:
- From the given options, the equation that matches our derived equation is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
This is the equation that properly represents the situation and can be used to find the value of [tex]\( x \)[/tex].
Here's how to approach the problem step-by-step:
1. Understand the Properties of an Isosceles Triangle:
- An isosceles triangle has two sides that are equal.
- If we denote the equal sides by [tex]\( x \)[/tex] and the base or shortest side by [tex]\( y \)[/tex], then in this case, the shortest side [tex]\( y \)[/tex] is given as 2.1 meters.
2. Use the Perimeter Formula:
- The perimeter of a triangle is the sum of the lengths of all its sides.
- For an isosceles triangle with equal sides [tex]\( x \)[/tex], the perimeter equation would be:
[tex]\[
\text{Perimeter} = x + x + y
\][/tex]
- This simplifies to:
[tex]\[
\text{Perimeter} = 2x + y
\][/tex]
3. Substitute the Known Values:
- The perimeter is given as 7.5 meters, and the shortest side [tex]\( y \)[/tex] is 2.1 meters.
- Substitute these values into the perimeter equation:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
4. Select the Correct Equation:
- From the given options, the equation that matches our derived equation is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
This is the equation that properly represents the situation and can be used to find the value of [tex]\( x \)[/tex].
