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Answer :
To solve the problem of finding the equation to determine the value of [tex]\( x \)[/tex] in the isosceles triangle with a perimeter of 7.5 meters, follow these steps:
1. Understand the structure of the isosceles triangle:
- In an isosceles triangle, two sides are of equal length, and the base is of a different length. In this problem, the two equal sides are represented by [tex]\( x \)[/tex], and the shortest side (the base) is represented by [tex]\( y \)[/tex].
2. Identify the given values:
- The perimeter of the triangle is 7.5 meters.
- The shortest side [tex]\( y \)[/tex] is given as 2.1 meters.
3. Write the equation for the perimeter:
- The perimeter of the triangle can be expressed as the sum of all its sides: [tex]\( 2x + y \)[/tex].
- Substituting the known value of [tex]\( y \)[/tex] into the perimeter equation gives you:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
4. Identify the correct equation from the given options:
- From the list of given equations, [tex]\( 2.1 + 2x = 7.5 \)[/tex] matches our derived equation [tex]\( 2x + 2.1 = 7.5 \)[/tex]. They are equivalent equations.
Thus, the correct equation to find the value of [tex]\( x \)[/tex] is [tex]\( 2.1 + 2x = 7.5 \)[/tex].
1. Understand the structure of the isosceles triangle:
- In an isosceles triangle, two sides are of equal length, and the base is of a different length. In this problem, the two equal sides are represented by [tex]\( x \)[/tex], and the shortest side (the base) is represented by [tex]\( y \)[/tex].
2. Identify the given values:
- The perimeter of the triangle is 7.5 meters.
- The shortest side [tex]\( y \)[/tex] is given as 2.1 meters.
3. Write the equation for the perimeter:
- The perimeter of the triangle can be expressed as the sum of all its sides: [tex]\( 2x + y \)[/tex].
- Substituting the known value of [tex]\( y \)[/tex] into the perimeter equation gives you:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
4. Identify the correct equation from the given options:
- From the list of given equations, [tex]\( 2.1 + 2x = 7.5 \)[/tex] matches our derived equation [tex]\( 2x + 2.1 = 7.5 \)[/tex]. They are equivalent equations.
Thus, the correct equation to find the value of [tex]\( x \)[/tex] is [tex]\( 2.1 + 2x = 7.5 \)[/tex].
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