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Answer :
To solve this problem, we need to determine which equation correctly represents the conditions given in the problem about the isosceles triangle.
1. Understand the properties of the isosceles triangle:
- An isosceles triangle has two sides that are equal in length, known as the legs. Let's denote the length of the equal sides as [tex]\( x \)[/tex].
- The third side, which is typically different, is given as 2.1 m. Let's denote this shortest side as [tex]\( y \)[/tex].
2. Given information:
- The perimeter of the triangle is 7.5 m.
- The shortest side, [tex]\( y \)[/tex], measures 2.1 m.
3. Set up the perimeter equation:
- The perimeter of a triangle is the sum of its three sides, which gives us:
[tex]\[
x + x + y = 7.5
\][/tex]
[tex]\[
2x + 2.1 = 7.5
\][/tex]
4. Identify the correct equation:
- The question provides different possible equations. We need to find which one matches the perimeter equation we derived:
- Option 1: [tex]\( 2x - 2.1 = 7.5 \)[/tex]
- Option 2: [tex]\( 4.2 + y = 7.5 \)[/tex]
- Option 3: [tex]\( y - 4.2 = 7.5 \)[/tex]
- Option 4: [tex]\( 2.1 + 2x = 7.5 \)[/tex]
5. Compare with the derived equation:
- Our derived equation is [tex]\( 2x + 2.1 = 7.5 \)[/tex].
- Analyzing the options, Option 4 [tex]\( (2.1 + 2x = 7.5) \)[/tex] corresponds exactly to this equation.
Thus, the correct equation to find the value of [tex]\( x \)[/tex] is [tex]\( 2.1 + 2x = 7.5 \)[/tex].
1. Understand the properties of the isosceles triangle:
- An isosceles triangle has two sides that are equal in length, known as the legs. Let's denote the length of the equal sides as [tex]\( x \)[/tex].
- The third side, which is typically different, is given as 2.1 m. Let's denote this shortest side as [tex]\( y \)[/tex].
2. Given information:
- The perimeter of the triangle is 7.5 m.
- The shortest side, [tex]\( y \)[/tex], measures 2.1 m.
3. Set up the perimeter equation:
- The perimeter of a triangle is the sum of its three sides, which gives us:
[tex]\[
x + x + y = 7.5
\][/tex]
[tex]\[
2x + 2.1 = 7.5
\][/tex]
4. Identify the correct equation:
- The question provides different possible equations. We need to find which one matches the perimeter equation we derived:
- Option 1: [tex]\( 2x - 2.1 = 7.5 \)[/tex]
- Option 2: [tex]\( 4.2 + y = 7.5 \)[/tex]
- Option 3: [tex]\( y - 4.2 = 7.5 \)[/tex]
- Option 4: [tex]\( 2.1 + 2x = 7.5 \)[/tex]
5. Compare with the derived equation:
- Our derived equation is [tex]\( 2x + 2.1 = 7.5 \)[/tex].
- Analyzing the options, Option 4 [tex]\( (2.1 + 2x = 7.5) \)[/tex] corresponds exactly to this equation.
Thus, the correct equation to find the value of [tex]\( x \)[/tex] is [tex]\( 2.1 + 2x = 7.5 \)[/tex].
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