Answer :
Here's how you can solve the given problem step-by-step:
1. Understand the Problem:
- We have an isosceles triangle with a total perimeter of 7.5 meters.
- In an isosceles triangle, two sides are of equal length. Let's call these sides "x".
- The shortest side of the triangle, which is different, measures 2.1 meters.
2. Set Up the Equation for Perimeter:
- The perimeter of a triangle is the sum of all its side lengths.
- For this isosceles triangle, the two equal sides are "x" and "x", and the shortest side is 2.1 meters.
- So, the equation for the perimeter is: [tex]\(x + x + 2.1 = 7.5\)[/tex].
3. Simplify the Equation:
- Combine the like terms (x terms) in the equation: [tex]\(2x + 2.1 = 7.5\)[/tex].
4. Solve for x:
- To isolate [tex]\(2x\)[/tex], subtract 2.1 from both sides of the equation:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
- Simplify the right side:
[tex]\[
2x = 5.4
\][/tex]
- Divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{5.4}{2}
\][/tex]
5. Calculate the Value of x:
- Perform the division:
[tex]\[
x = 2.7
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is 2.7 meters. The correct equation to find this value is [tex]\(2.1 + 2x = 7.5\)[/tex].
1. Understand the Problem:
- We have an isosceles triangle with a total perimeter of 7.5 meters.
- In an isosceles triangle, two sides are of equal length. Let's call these sides "x".
- The shortest side of the triangle, which is different, measures 2.1 meters.
2. Set Up the Equation for Perimeter:
- The perimeter of a triangle is the sum of all its side lengths.
- For this isosceles triangle, the two equal sides are "x" and "x", and the shortest side is 2.1 meters.
- So, the equation for the perimeter is: [tex]\(x + x + 2.1 = 7.5\)[/tex].
3. Simplify the Equation:
- Combine the like terms (x terms) in the equation: [tex]\(2x + 2.1 = 7.5\)[/tex].
4. Solve for x:
- To isolate [tex]\(2x\)[/tex], subtract 2.1 from both sides of the equation:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
- Simplify the right side:
[tex]\[
2x = 5.4
\][/tex]
- Divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{5.4}{2}
\][/tex]
5. Calculate the Value of x:
- Perform the division:
[tex]\[
x = 2.7
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is 2.7 meters. The correct equation to find this value is [tex]\(2.1 + 2x = 7.5\)[/tex].
