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Answer :
To solve this problem, we need to find the correct equation among the given options that can be used to determine the value of [tex]\( x \)[/tex] for an isosceles triangle with a perimeter of 7.5 meters and a shortest side measuring 2.1 meters.
In an isosceles triangle, two sides are of equal length. Let's assume these equal sides have a length of [tex]\( x \)[/tex]. The third side, which is the shortest, is given as [tex]\( y = 2.1 \)[/tex] meters. According to the problem, the perimeter is 7.5 meters.
The formula for the perimeter of a triangle is the sum of all its sides. For this isosceles triangle, the equation can be set up as follows:
[tex]\[ 2x + y = 7.5 \][/tex]
Substituting the value of [tex]\( y \)[/tex] (the shortest side) into the equation gives:
[tex]\[ 2x + 2.1 = 7.5 \][/tex]
We can now see that this matches one of the provided options:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
This equation is correct because it represents the perimeter of the isosceles triangle in terms of the lengths of its sides. Therefore, the equation we can use to find the value of [tex]\( x \)[/tex] is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
In an isosceles triangle, two sides are of equal length. Let's assume these equal sides have a length of [tex]\( x \)[/tex]. The third side, which is the shortest, is given as [tex]\( y = 2.1 \)[/tex] meters. According to the problem, the perimeter is 7.5 meters.
The formula for the perimeter of a triangle is the sum of all its sides. For this isosceles triangle, the equation can be set up as follows:
[tex]\[ 2x + y = 7.5 \][/tex]
Substituting the value of [tex]\( y \)[/tex] (the shortest side) into the equation gives:
[tex]\[ 2x + 2.1 = 7.5 \][/tex]
We can now see that this matches one of the provided options:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
This equation is correct because it represents the perimeter of the isosceles triangle in terms of the lengths of its sides. Therefore, the equation we can use to find the value of [tex]\( x \)[/tex] is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
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