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Answer :
To solve this problem, we need to determine which equation can be used to find the value of [tex]\( x \)[/tex], which represents the length of each of the two equal sides of the isosceles triangle.
Here's the step-by-step explanation:
1. Understand the Problem:
- We have an isosceles triangle, which means it has two sides of equal length. Let's denote these sides each as [tex]\( x \)[/tex].
- The shortest side of the triangle is given as [tex]\( y = 2.1 \)[/tex] meters.
- The perimeter of the triangle is the sum of all its sides and is given as [tex]\( 7.5 \)[/tex] meters.
2. Express the Perimeter:
- The perimeter of the triangle is composed of the two equal sides plus the shortest side. Therefore, the expression for the perimeter is:
[tex]\[
\text{Perimeter} = x + x + y = 2x + y
\][/tex]
3. Set Up the Equation:
- Since we know the perimeter is 7.5 meters, we can set up the equation:
[tex]\[
2x + y = 7.5
\][/tex]
4. Substitute the Known Value:
- We know [tex]\( y = 2.1 \)[/tex] meters, so substitute [tex]\( y \)[/tex] into the equation:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
5. Solve for [tex]\( x \)[/tex]:
- Rearrange the equation to solve for [tex]\( x \)[/tex]:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
6. Calculate:
- Calculate the right-hand side:
[tex]\[
2x = 5.4
\][/tex]
- Divide by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 2.7
\][/tex]
Therefore, the equation that can be used to find [tex]\( x \)[/tex] is [tex]\( 2x + 2.1 = 7.5 \)[/tex]. The length of each of the equal sides, [tex]\( x \)[/tex], is 2.7 meters.
Here's the step-by-step explanation:
1. Understand the Problem:
- We have an isosceles triangle, which means it has two sides of equal length. Let's denote these sides each as [tex]\( x \)[/tex].
- The shortest side of the triangle is given as [tex]\( y = 2.1 \)[/tex] meters.
- The perimeter of the triangle is the sum of all its sides and is given as [tex]\( 7.5 \)[/tex] meters.
2. Express the Perimeter:
- The perimeter of the triangle is composed of the two equal sides plus the shortest side. Therefore, the expression for the perimeter is:
[tex]\[
\text{Perimeter} = x + x + y = 2x + y
\][/tex]
3. Set Up the Equation:
- Since we know the perimeter is 7.5 meters, we can set up the equation:
[tex]\[
2x + y = 7.5
\][/tex]
4. Substitute the Known Value:
- We know [tex]\( y = 2.1 \)[/tex] meters, so substitute [tex]\( y \)[/tex] into the equation:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
5. Solve for [tex]\( x \)[/tex]:
- Rearrange the equation to solve for [tex]\( x \)[/tex]:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
6. Calculate:
- Calculate the right-hand side:
[tex]\[
2x = 5.4
\][/tex]
- Divide by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 2.7
\][/tex]
Therefore, the equation that can be used to find [tex]\( x \)[/tex] is [tex]\( 2x + 2.1 = 7.5 \)[/tex]. The length of each of the equal sides, [tex]\( x \)[/tex], is 2.7 meters.
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