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Answer :
To solve for the value of [tex]\( x \)[/tex] in the given isosceles triangle problem where the perimeter is 7.5 meters and the shortest side [tex]\( y \)[/tex] measures 2.1 meters, follow these steps:
1. Understand the Triangle's Properties:
An isosceles triangle has at least two sides that are equal in length. Let's denote the two equal sides of the triangle as [tex]\( x \)[/tex].
2. Express the Perimeter:
The perimeter of the triangle is the sum of all its sides. So, you can write the equation for the perimeter as:
[tex]\[
x + x + y = 7.5
\][/tex]
Since we know [tex]\( y = 2.1 \)[/tex], substitute this value into the equation:
[tex]\[
x + x + 2.1 = 7.5
\][/tex]
This simplifies to:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
To find [tex]\( x \)[/tex], you need to isolate it on one side of the equation. Start by subtracting 2.1 from both sides:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
After performing the subtraction:
[tex]\[
2x = 5.4
\][/tex]
Finally, divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5.4}{2} = 2.7
\][/tex]
So, the value of [tex]\( x \)[/tex] is 2.7 meters. The correct equation used to find [tex]\( x \)[/tex] is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
1. Understand the Triangle's Properties:
An isosceles triangle has at least two sides that are equal in length. Let's denote the two equal sides of the triangle as [tex]\( x \)[/tex].
2. Express the Perimeter:
The perimeter of the triangle is the sum of all its sides. So, you can write the equation for the perimeter as:
[tex]\[
x + x + y = 7.5
\][/tex]
Since we know [tex]\( y = 2.1 \)[/tex], substitute this value into the equation:
[tex]\[
x + x + 2.1 = 7.5
\][/tex]
This simplifies to:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
To find [tex]\( x \)[/tex], you need to isolate it on one side of the equation. Start by subtracting 2.1 from both sides:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
After performing the subtraction:
[tex]\[
2x = 5.4
\][/tex]
Finally, divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5.4}{2} = 2.7
\][/tex]
So, the value of [tex]\( x \)[/tex] is 2.7 meters. The correct equation used to find [tex]\( x \)[/tex] is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
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