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Answer :
To solve this problem, we need to find the equation that can be used to determine the value of [tex]\( x \)[/tex] in an isosceles triangle with a given perimeter of 7.5 meters.
Here's how you can think through the problem:
1. Understanding Isosceles Triangle:
An isosceles triangle has two sides that are equal in length. If we let these equal sides each be [tex]\( x \)[/tex], the shortest side will be [tex]\( y \)[/tex].
2. Given Information:
- The shortest side [tex]\( y \)[/tex] is 2.1 meters.
- The perimeter of the triangle is 7.5 meters.
3. Setting up the Perimeter Equation:
The perimeter of a triangle is the sum of the lengths of all its sides. Therefore, the equation for the perimeter is:
[tex]\[
x + x + y = \text{perimeter}
\][/tex]
4. Substitute the Given Values:
- Since [tex]\( y = 2.1 \)[/tex] meters, substitute this into the equation:
[tex]\[
x + x + 2.1 = 7.5
\][/tex]
- Simplify by combining like terms:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
5. Final Equation:
Therefore, the equation used to find [tex]\( x \)[/tex] is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
In conclusion, the correct equation is [tex]\( 2.1 + 2x = 7.5 \)[/tex]. This represents the sum of the two equal sides and the shortest side equating to the given perimeter of the triangle.
Here's how you can think through the problem:
1. Understanding Isosceles Triangle:
An isosceles triangle has two sides that are equal in length. If we let these equal sides each be [tex]\( x \)[/tex], the shortest side will be [tex]\( y \)[/tex].
2. Given Information:
- The shortest side [tex]\( y \)[/tex] is 2.1 meters.
- The perimeter of the triangle is 7.5 meters.
3. Setting up the Perimeter Equation:
The perimeter of a triangle is the sum of the lengths of all its sides. Therefore, the equation for the perimeter is:
[tex]\[
x + x + y = \text{perimeter}
\][/tex]
4. Substitute the Given Values:
- Since [tex]\( y = 2.1 \)[/tex] meters, substitute this into the equation:
[tex]\[
x + x + 2.1 = 7.5
\][/tex]
- Simplify by combining like terms:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
5. Final Equation:
Therefore, the equation used to find [tex]\( x \)[/tex] is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
In conclusion, the correct equation is [tex]\( 2.1 + 2x = 7.5 \)[/tex]. This represents the sum of the two equal sides and the shortest side equating to the given perimeter of the triangle.
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