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Answer :
To solve this problem, let's break down the information provided:
1. We have an isosceles triangle with a perimeter of 7.5 meters.
2. In an isosceles triangle, two sides are equal. We are told the shortest side, [tex]\( y \)[/tex], measures 2.1 meters. This shortest side is not one of the equal sides, so the other two sides are the ones that are equal.
Based on this information, we can set up an equation:
- The perimeter of a triangle is the sum of all its sides.
- Therefore, for the isosceles triangle with sides of length [tex]\( x, x, \)[/tex] and [tex]\( y \)[/tex], the equation for the perimeter is:
[tex]\[
x + x + y = 7.5
\][/tex]
Simplifying this, we get:
[tex]\[
2x + y = 7.5
\][/tex]
Given that [tex]\( y = 2.1 \)[/tex], we substitute this value into the equation:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
The equation above directly matches the choice: [tex]\(2.1 + 2x = 7.5\)[/tex].
To find [tex]\( x \)[/tex], solve the equation:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
[tex]\[
2x = 5.4
\][/tex]
Divide both sides by 2 to isolate [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5.4}{2}
\][/tex]
[tex]\[
x = 2.7
\][/tex]
So, the value of [tex]\( x \)[/tex] is 2.7 meters. Therefore, the correct equation to find [tex]\( x \)[/tex] is [tex]\(2.1 + 2x = 7.5\)[/tex].
1. We have an isosceles triangle with a perimeter of 7.5 meters.
2. In an isosceles triangle, two sides are equal. We are told the shortest side, [tex]\( y \)[/tex], measures 2.1 meters. This shortest side is not one of the equal sides, so the other two sides are the ones that are equal.
Based on this information, we can set up an equation:
- The perimeter of a triangle is the sum of all its sides.
- Therefore, for the isosceles triangle with sides of length [tex]\( x, x, \)[/tex] and [tex]\( y \)[/tex], the equation for the perimeter is:
[tex]\[
x + x + y = 7.5
\][/tex]
Simplifying this, we get:
[tex]\[
2x + y = 7.5
\][/tex]
Given that [tex]\( y = 2.1 \)[/tex], we substitute this value into the equation:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
The equation above directly matches the choice: [tex]\(2.1 + 2x = 7.5\)[/tex].
To find [tex]\( x \)[/tex], solve the equation:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
[tex]\[
2x = 5.4
\][/tex]
Divide both sides by 2 to isolate [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5.4}{2}
\][/tex]
[tex]\[
x = 2.7
\][/tex]
So, the value of [tex]\( x \)[/tex] is 2.7 meters. Therefore, the correct equation to find [tex]\( x \)[/tex] is [tex]\(2.1 + 2x = 7.5\)[/tex].
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