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Answer :
To solve the problem of finding the value of [tex]\( x \)[/tex], we need to understand the structure of the given isosceles triangle:
1. Understand the Triangle: Given isosceles triangle has two equal sides, and one of them is the shortest side [tex]\( y = 2.1 \, \text{m} \)[/tex].
2. Perimeter: The perimeter of the triangle is the sum of all three sides, and it is given as [tex]\( 7.5 \, \text{m} \)[/tex].
3. Setting Up the Equation: In an isosceles triangle, let the two equal sides each be [tex]\( x \)[/tex]. Since the triangle is isosceles, it makes sense that the two longer sides are equal.
Now, the equation for the perimeter is:
[tex]\[ y + 2x = 7.5 \][/tex]
Substitute [tex]\( y = 2.1 \, \text{m} \)[/tex] into the equation:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
This is the correct equation that models the situation.
4. Finding [tex]\( x \)[/tex]: Solve for [tex]\( x \)[/tex] by isolating it in the equation:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
[tex]\[
2x = 5.4
\][/tex]
Divide both sides by 2:
[tex]\[
x = \frac{5.4}{2} = 2.7
\][/tex]
Therefore, the correct equation to find [tex]\( x \)[/tex] is [tex]\( 2.1 + 2x = 7.5 \)[/tex], and [tex]\( x \)[/tex] evaluates to [tex]\( 2.7 \, \text{m} \)[/tex].
1. Understand the Triangle: Given isosceles triangle has two equal sides, and one of them is the shortest side [tex]\( y = 2.1 \, \text{m} \)[/tex].
2. Perimeter: The perimeter of the triangle is the sum of all three sides, and it is given as [tex]\( 7.5 \, \text{m} \)[/tex].
3. Setting Up the Equation: In an isosceles triangle, let the two equal sides each be [tex]\( x \)[/tex]. Since the triangle is isosceles, it makes sense that the two longer sides are equal.
Now, the equation for the perimeter is:
[tex]\[ y + 2x = 7.5 \][/tex]
Substitute [tex]\( y = 2.1 \, \text{m} \)[/tex] into the equation:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
This is the correct equation that models the situation.
4. Finding [tex]\( x \)[/tex]: Solve for [tex]\( x \)[/tex] by isolating it in the equation:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
[tex]\[
2x = 5.4
\][/tex]
Divide both sides by 2:
[tex]\[
x = \frac{5.4}{2} = 2.7
\][/tex]
Therefore, the correct equation to find [tex]\( x \)[/tex] is [tex]\( 2.1 + 2x = 7.5 \)[/tex], and [tex]\( x \)[/tex] evaluates to [tex]\( 2.7 \, \text{m} \)[/tex].
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