Answer :
To solve this problem and find the value of [tex]\( x \)[/tex] in the isosceles triangle, let's start by understanding what we are given and what we need to find:
- The triangle is isosceles, which means it has two equal sides.
- The perimeter of the triangle is 7.5 meters.
- The shortest side, [tex]\( y \)[/tex], measures 2.1 meters.
In an isosceles triangle, the perimeter is the sum of all its sides. Therefore, we can express the perimeter using the equation:
[tex]\[ 2x + y = \text{perimeter} \][/tex]
Here, [tex]\( x \)[/tex] represents the length of each of the equal sides. With the given values:
[tex]\[ 2x + 2.1 = 7.5 \][/tex]
Now, we need to solve this equation for [tex]\( x \)[/tex].
1. Start with the equation:
[tex]\[ 2x + 2.1 = 7.5 \][/tex]
2. Subtract 2.1 from both sides to isolate the terms with [tex]\( x \)[/tex] on one side:
[tex]\[ 2x = 7.5 - 2.1 \][/tex]
3. Calculate the right-hand side:
[tex]\[ 2x = 5.4 \][/tex]
4. Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{5.4}{2} \][/tex]
5. Calculate the division:
[tex]\[ x = 2.7 \][/tex]
So, the value of [tex]\( x \)[/tex] is 2.7 meters. The correct equation to use in this context is [tex]\( 2.1 + 2x = 7.5 \)[/tex].
- The triangle is isosceles, which means it has two equal sides.
- The perimeter of the triangle is 7.5 meters.
- The shortest side, [tex]\( y \)[/tex], measures 2.1 meters.
In an isosceles triangle, the perimeter is the sum of all its sides. Therefore, we can express the perimeter using the equation:
[tex]\[ 2x + y = \text{perimeter} \][/tex]
Here, [tex]\( x \)[/tex] represents the length of each of the equal sides. With the given values:
[tex]\[ 2x + 2.1 = 7.5 \][/tex]
Now, we need to solve this equation for [tex]\( x \)[/tex].
1. Start with the equation:
[tex]\[ 2x + 2.1 = 7.5 \][/tex]
2. Subtract 2.1 from both sides to isolate the terms with [tex]\( x \)[/tex] on one side:
[tex]\[ 2x = 7.5 - 2.1 \][/tex]
3. Calculate the right-hand side:
[tex]\[ 2x = 5.4 \][/tex]
4. Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{5.4}{2} \][/tex]
5. Calculate the division:
[tex]\[ x = 2.7 \][/tex]
So, the value of [tex]\( x \)[/tex] is 2.7 meters. The correct equation to use in this context is [tex]\( 2.1 + 2x = 7.5 \)[/tex].
