Answer :
Certainly! Let's work through the problem together step by step.
We have an isosceles triangle with a perimeter of 7.5 meters. In an isosceles triangle, two sides are equal in length, and we are given that the shortest side, [tex]\( y \)[/tex], measures 2.1 meters. We need to find an equation that helps us determine the length of the equal sides, which are represented as [tex]\( x \)[/tex].
### Step-by-Step Solution:
1. Understand the Perimeter Formula:
- The perimeter of a triangle is the sum of the lengths of its sides.
- For an isosceles triangle with two equal sides, the formula becomes:
[tex]\[
\text{Perimeter} = 2 \times x + y
\][/tex]
- We know the perimeter is 7.5 meters and [tex]\( y = 2.1 \)[/tex] meters.
2. Set Up the Equation:
- Plug the known values into the perimeter formula:
[tex]\[
7.5 = 2 \times x + 2.1
\][/tex]
- This is the equation you can use to find [tex]\( x \)[/tex].
3. Selecting the Correct Option:
- Among the given options, the equation that matches our setup is:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
- Now we solve the equation to find the value of [tex]\( x \)[/tex].
- First, subtract 2.1 from both sides:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
[tex]\[
2x = 5.4
\][/tex]
- Next, divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5.4}{2} = 2.7
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is 2.7 meters, and the correct equation to find [tex]\( x \)[/tex] is [tex]\( 2x + 2.1 = 7.5 \)[/tex].
We have an isosceles triangle with a perimeter of 7.5 meters. In an isosceles triangle, two sides are equal in length, and we are given that the shortest side, [tex]\( y \)[/tex], measures 2.1 meters. We need to find an equation that helps us determine the length of the equal sides, which are represented as [tex]\( x \)[/tex].
### Step-by-Step Solution:
1. Understand the Perimeter Formula:
- The perimeter of a triangle is the sum of the lengths of its sides.
- For an isosceles triangle with two equal sides, the formula becomes:
[tex]\[
\text{Perimeter} = 2 \times x + y
\][/tex]
- We know the perimeter is 7.5 meters and [tex]\( y = 2.1 \)[/tex] meters.
2. Set Up the Equation:
- Plug the known values into the perimeter formula:
[tex]\[
7.5 = 2 \times x + 2.1
\][/tex]
- This is the equation you can use to find [tex]\( x \)[/tex].
3. Selecting the Correct Option:
- Among the given options, the equation that matches our setup is:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
- Now we solve the equation to find the value of [tex]\( x \)[/tex].
- First, subtract 2.1 from both sides:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
[tex]\[
2x = 5.4
\][/tex]
- Next, divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5.4}{2} = 2.7
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is 2.7 meters, and the correct equation to find [tex]\( x \)[/tex] is [tex]\( 2x + 2.1 = 7.5 \)[/tex].
