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Answer :
To solve the problem, we need to find the correct equation that represents the perimeter of an isosceles triangle given its shortest side and total perimeter.
Here's the step-by-step solution:
1. Identify given values:
- The perimeter of the isosceles triangle is [tex]\(7.5\)[/tex] meters.
- The shortest side [tex]\(y\)[/tex] measures [tex]\(2.1\)[/tex] meters.
2. Understand the properties of an isosceles triangle:
- An isosceles triangle has two equal sides and one different side.
- Since the shortest side [tex]\(y\)[/tex] is [tex]\(2.1\)[/tex] meters, it must be the 'base' of the triangle (the different side).
- Let the equal sides be represented by [tex]\(x\)[/tex].
3. Use the formula for the perimeter of a triangle:
- The perimeter of a triangle is the sum of all its sides.
- For our isosceles triangle, the perimeter [tex]\(P\)[/tex] can be expressed as:
[tex]\[
P = x + x + y
\][/tex]
- Simplifying, this becomes:
[tex]\[
P = 2x + y
\][/tex]
4. Substitute the known values into the equation:
- The perimeter [tex]\(P\)[/tex] is [tex]\(7.5\)[/tex] meters, and the shortest side [tex]\(y\)[/tex] is [tex]\(2.1\)[/tex] meters.
- Substitute these values into the perimeter equation:
[tex]\[
7.5 = 2x + 2.1
\][/tex]
5. Rearrange this equation to match one of the given choices:
- Subtract [tex]\(2.1\)[/tex] from both sides to isolate the terms with [tex]\(x\)[/tex]:
[tex]\[
7.5 - 2.1 = 2x
\][/tex]
- Simplifying the left-hand side:
[tex]\[
5.4 = 2x
\][/tex]
Alternatively, we can express it as:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
6. Identify the correct answer:
- The correct equation is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
Therefore, the correct equation to use to find the value of [tex]\(x\)[/tex] is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
Here's the step-by-step solution:
1. Identify given values:
- The perimeter of the isosceles triangle is [tex]\(7.5\)[/tex] meters.
- The shortest side [tex]\(y\)[/tex] measures [tex]\(2.1\)[/tex] meters.
2. Understand the properties of an isosceles triangle:
- An isosceles triangle has two equal sides and one different side.
- Since the shortest side [tex]\(y\)[/tex] is [tex]\(2.1\)[/tex] meters, it must be the 'base' of the triangle (the different side).
- Let the equal sides be represented by [tex]\(x\)[/tex].
3. Use the formula for the perimeter of a triangle:
- The perimeter of a triangle is the sum of all its sides.
- For our isosceles triangle, the perimeter [tex]\(P\)[/tex] can be expressed as:
[tex]\[
P = x + x + y
\][/tex]
- Simplifying, this becomes:
[tex]\[
P = 2x + y
\][/tex]
4. Substitute the known values into the equation:
- The perimeter [tex]\(P\)[/tex] is [tex]\(7.5\)[/tex] meters, and the shortest side [tex]\(y\)[/tex] is [tex]\(2.1\)[/tex] meters.
- Substitute these values into the perimeter equation:
[tex]\[
7.5 = 2x + 2.1
\][/tex]
5. Rearrange this equation to match one of the given choices:
- Subtract [tex]\(2.1\)[/tex] from both sides to isolate the terms with [tex]\(x\)[/tex]:
[tex]\[
7.5 - 2.1 = 2x
\][/tex]
- Simplifying the left-hand side:
[tex]\[
5.4 = 2x
\][/tex]
Alternatively, we can express it as:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
6. Identify the correct answer:
- The correct equation is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
Therefore, the correct equation to use to find the value of [tex]\(x\)[/tex] is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
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