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Answer :
To find the value of [tex]\( x \)[/tex] in the isosceles triangle with a perimeter of 7.5 meters, and where the shortest side [tex]\( y \)[/tex] is 2.1 meters, we can set up the problem as follows:
1. Understand the Triangle's Sides: In an isosceles triangle, two sides are equal, let's call them [tex]\( x \)[/tex]. The third side, given here, is [tex]\( y = 2.1 \)[/tex] meters.
2. Express the Perimeter: The perimeter of the triangle can be expressed as:
[tex]\[
\text{Perimeter} = x + x + y = 2x + y
\][/tex]
3. Substitute Known Values:
- The perimeter is given as 7.5 meters.
- Substitute [tex]\( y = 2.1 \)[/tex] meters into the equation:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
- First, subtract 2.1 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
- Calculate the right side:
[tex]\[
2x = 5.4
\][/tex]
This equation [tex]\( 2x = 5.4 \)[/tex] can now be used to find the value of [tex]\( x \)[/tex]. The equation that helps us find [tex]\( x \)[/tex] is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
This is the correct equation from the given choices to solve for [tex]\( x \)[/tex].
1. Understand the Triangle's Sides: In an isosceles triangle, two sides are equal, let's call them [tex]\( x \)[/tex]. The third side, given here, is [tex]\( y = 2.1 \)[/tex] meters.
2. Express the Perimeter: The perimeter of the triangle can be expressed as:
[tex]\[
\text{Perimeter} = x + x + y = 2x + y
\][/tex]
3. Substitute Known Values:
- The perimeter is given as 7.5 meters.
- Substitute [tex]\( y = 2.1 \)[/tex] meters into the equation:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
- First, subtract 2.1 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
- Calculate the right side:
[tex]\[
2x = 5.4
\][/tex]
This equation [tex]\( 2x = 5.4 \)[/tex] can now be used to find the value of [tex]\( x \)[/tex]. The equation that helps us find [tex]\( x \)[/tex] is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
This is the correct equation from the given choices to solve for [tex]\( x \)[/tex].
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Rewritten by : Jeany
