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Answer :
To solve this problem, we need to find out which equation correctly represents the relationship among the sides of the isosceles triangle given its perimeter and the shortest side.
Here's what we know:
- The triangle is isosceles, meaning it has two equal-length sides.
- The perimeter of the triangle is 7.5 meters.
- The shortest side [tex]\( y \)[/tex] measures 2.1 meters.
Since it's an isosceles triangle, let's assume the two equal sides are both of length [tex]\( x \)[/tex]. The equation for the perimeter of the triangle, or the sum of all its sides, is given by:
[tex]\[ 2x + y = 7.5 \][/tex]
Since [tex]\( y \)[/tex] is the shortest side measuring 2.1 meters, we can substitute [tex]\( y \)[/tex] with 2.1 in the equation:
[tex]\[ 2x + 2.1 = 7.5 \][/tex]
This gives us the equation we need to use to find [tex]\( x \)[/tex]. From the options given:
1. [tex]\( 2x - 2.1 = 7.5 \)[/tex]
2. [tex]\( 4.2 + y = 7.5 \)[/tex]
3. [tex]\( y - 4.2 = 7.5 \)[/tex]
4. [tex]\( 2.1 + 2x = 7.5 \)[/tex]
The correct equation that represents this relationship is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
So, the correct answer is:
[tex]\( 2.1 + 2x = 7.5 \)[/tex]
Here's what we know:
- The triangle is isosceles, meaning it has two equal-length sides.
- The perimeter of the triangle is 7.5 meters.
- The shortest side [tex]\( y \)[/tex] measures 2.1 meters.
Since it's an isosceles triangle, let's assume the two equal sides are both of length [tex]\( x \)[/tex]. The equation for the perimeter of the triangle, or the sum of all its sides, is given by:
[tex]\[ 2x + y = 7.5 \][/tex]
Since [tex]\( y \)[/tex] is the shortest side measuring 2.1 meters, we can substitute [tex]\( y \)[/tex] with 2.1 in the equation:
[tex]\[ 2x + 2.1 = 7.5 \][/tex]
This gives us the equation we need to use to find [tex]\( x \)[/tex]. From the options given:
1. [tex]\( 2x - 2.1 = 7.5 \)[/tex]
2. [tex]\( 4.2 + y = 7.5 \)[/tex]
3. [tex]\( y - 4.2 = 7.5 \)[/tex]
4. [tex]\( 2.1 + 2x = 7.5 \)[/tex]
The correct equation that represents this relationship is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
So, the correct answer is:
[tex]\( 2.1 + 2x = 7.5 \)[/tex]
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