Answer :
To solve this problem, we're dealing with an isosceles triangle, which has two equal sides. The perimeter of the triangle is the total length around it, which is given as 7.5 meters. One side of the triangle, which is the shortest side [tex]\( y \)[/tex], measures 2.1 meters. Our goal is to find the equation that helps determine the value of [tex]\( x \)[/tex], the length of each of the equal sides.
Here’s how you can think through this:
1. Understand the Perimeter Equation:
- The perimeter of any triangle is the sum of the lengths of its three sides. In an isosceles triangle, the perimeter [tex]\( P \)[/tex] can be written as:
[tex]\[
P = x + x + y
\][/tex]
Where [tex]\( x \)[/tex] is the length of each of the equal sides, and [tex]\( y \)[/tex] is the length of the base or shortest side.
2. Insert the Known Values:
- We know the perimeter is 7.5 meters and [tex]\( y \)[/tex] is 2.1 meters, so we can substitute these into the equation:
[tex]\[
7.5 = 2x + 2.1
\][/tex]
3. Identify the Correct Equation:
- We need the equation that represents this situation:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
- To isolate [tex]\( x \)[/tex], subtract 2.1 from both sides of the equation:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
- Calculate [tex]\( 7.5 - 2.1 \)[/tex] which equals 5.4, so:
[tex]\[
2x = 5.4
\][/tex]
- Finally, divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5.4}{2} = 2.7
\][/tex]
Therefore, the equation [tex]\( 2.1 + 2x = 7.5 \)[/tex] is the correct one to find the length of the equal sides in the triangle.
Here’s how you can think through this:
1. Understand the Perimeter Equation:
- The perimeter of any triangle is the sum of the lengths of its three sides. In an isosceles triangle, the perimeter [tex]\( P \)[/tex] can be written as:
[tex]\[
P = x + x + y
\][/tex]
Where [tex]\( x \)[/tex] is the length of each of the equal sides, and [tex]\( y \)[/tex] is the length of the base or shortest side.
2. Insert the Known Values:
- We know the perimeter is 7.5 meters and [tex]\( y \)[/tex] is 2.1 meters, so we can substitute these into the equation:
[tex]\[
7.5 = 2x + 2.1
\][/tex]
3. Identify the Correct Equation:
- We need the equation that represents this situation:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
- To isolate [tex]\( x \)[/tex], subtract 2.1 from both sides of the equation:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
- Calculate [tex]\( 7.5 - 2.1 \)[/tex] which equals 5.4, so:
[tex]\[
2x = 5.4
\][/tex]
- Finally, divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5.4}{2} = 2.7
\][/tex]
Therefore, the equation [tex]\( 2.1 + 2x = 7.5 \)[/tex] is the correct one to find the length of the equal sides in the triangle.
