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Answer :
To solve the problem of finding the value of [tex]\( x \)[/tex] in an isosceles triangle with a perimeter of 7.5 meters, where the shortest side [tex]\( y \)[/tex] measures 2.1 meters, follow these steps:
1. Understand the Properties of the Isosceles Triangle:
An isosceles triangle has two sides of equal length. Let's assume that the equal sides are both [tex]\( x \)[/tex]. The shortest side, given as [tex]\( y \)[/tex], measures 2.1 meters.
2. Formulate the Equation for Perimeter:
The perimeter of the triangle is the sum of all its sides. Hence, the equation for the perimeter is:
[tex]\[
x + x + y = 7.5
\][/tex]
Simplifying the expression gives:
[tex]\[
2x + y = 7.5
\][/tex]
3. Substitute the Known Value of [tex]\( y \)[/tex]:
We know [tex]\( y = 2.1 \)[/tex], so substitute this into the equation:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
To isolate [tex]\( x \)[/tex], first subtract 2.1 from both sides of the equation:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
[tex]\[
2x = 5.4
\][/tex]
5. Divide Each Side by 2:
Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5.4}{2}
\][/tex]
[tex]\[
x = 2.7
\][/tex]
Thus, the equation that can be used to find the value of [tex]\( x \)[/tex] is [tex]\( 2.1 + 2x = 7.5 \)[/tex], and solving it gives us [tex]\( x = 2.7 \)[/tex] meters.
1. Understand the Properties of the Isosceles Triangle:
An isosceles triangle has two sides of equal length. Let's assume that the equal sides are both [tex]\( x \)[/tex]. The shortest side, given as [tex]\( y \)[/tex], measures 2.1 meters.
2. Formulate the Equation for Perimeter:
The perimeter of the triangle is the sum of all its sides. Hence, the equation for the perimeter is:
[tex]\[
x + x + y = 7.5
\][/tex]
Simplifying the expression gives:
[tex]\[
2x + y = 7.5
\][/tex]
3. Substitute the Known Value of [tex]\( y \)[/tex]:
We know [tex]\( y = 2.1 \)[/tex], so substitute this into the equation:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
To isolate [tex]\( x \)[/tex], first subtract 2.1 from both sides of the equation:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
[tex]\[
2x = 5.4
\][/tex]
5. Divide Each Side by 2:
Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5.4}{2}
\][/tex]
[tex]\[
x = 2.7
\][/tex]
Thus, the equation that can be used to find the value of [tex]\( x \)[/tex] is [tex]\( 2.1 + 2x = 7.5 \)[/tex], and solving it gives us [tex]\( x = 2.7 \)[/tex] meters.
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