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Answer :
To find the value of [tex]\( x \)[/tex] for the given isosceles triangle, let's break down the problem step-by-step.
1. Understand the properties of the isosceles triangle: In an isosceles triangle, two sides are of equal length.
2. Identify the given information:
- The perimeter of the triangle is [tex]\( 7.5 \)[/tex] meters.
- The shortest side, denoted as [tex]\( y \)[/tex], measures [tex]\( 2.1 \)[/tex] meters.
3. Set up the equation for the perimeter:
- Since it's an isosceles triangle, let's assume the two equal sides are [tex]\( x \)[/tex].
- The formula for the perimeter, which is the sum of all sides, is:
[tex]\[
x + x + y = 7.5
\][/tex]
4. Substitute the known value:
- Replace [tex]\( y \)[/tex] with [tex]\( 2.1 \)[/tex]:
[tex]\[
x + x + 2.1 = 7.5
\][/tex]
5. Simplify the equation:
- Combine like terms:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
6. Identify the correct equation:
- From the options provided, the equation that matches this is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
This equation will allow you to solve for [tex]\( x \)[/tex] when you need to find its value.
1. Understand the properties of the isosceles triangle: In an isosceles triangle, two sides are of equal length.
2. Identify the given information:
- The perimeter of the triangle is [tex]\( 7.5 \)[/tex] meters.
- The shortest side, denoted as [tex]\( y \)[/tex], measures [tex]\( 2.1 \)[/tex] meters.
3. Set up the equation for the perimeter:
- Since it's an isosceles triangle, let's assume the two equal sides are [tex]\( x \)[/tex].
- The formula for the perimeter, which is the sum of all sides, is:
[tex]\[
x + x + y = 7.5
\][/tex]
4. Substitute the known value:
- Replace [tex]\( y \)[/tex] with [tex]\( 2.1 \)[/tex]:
[tex]\[
x + x + 2.1 = 7.5
\][/tex]
5. Simplify the equation:
- Combine like terms:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
6. Identify the correct equation:
- From the options provided, the equation that matches this is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
This equation will allow you to solve for [tex]\( x \)[/tex] when you need to find its value.
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Rewritten by : Jeany
