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Answer :
Certainly! To solve the problem of finding the value of [tex]\( x \)[/tex] in an isosceles triangle with a given perimeter and shortest side, let's work through the information step-by-step:
1. Understanding the Triangle:
An isosceles triangle has two sides that are of equal length and one side that is different. In this problem, the side that is different is the shortest side, which measures [tex]\( y = 2.1 \)[/tex] meters.
2. Perimeter of the Triangle:
The perimeter of the triangle is given as [tex]\( 7.5 \)[/tex] meters. The perimeter of any triangle is the sum of its three sides.
3. Express the Perimeter Using Side Lengths:
Since the triangle is isosceles, let's assume the two equal sides have a length of [tex]\( x \)[/tex]. We can write the equation for the perimeter as:
[tex]\[
x + x + y = 7.5
\][/tex]
Simplifying, this becomes:
[tex]\[
2x + y = 7.5
\][/tex]
4. Substitute the Known Value of [tex]\( y \)[/tex]:
We know that the shortest side [tex]\( y \)[/tex] is [tex]\( 2.1 \)[/tex] meters. Substitute this into the perimeter equation:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
Thus, the equation that can be used to find the value of [tex]\( x \)[/tex] is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
This equation correctly represents the relationship between the lengths of the sides in the isosceles triangle and its given perimeter.
1. Understanding the Triangle:
An isosceles triangle has two sides that are of equal length and one side that is different. In this problem, the side that is different is the shortest side, which measures [tex]\( y = 2.1 \)[/tex] meters.
2. Perimeter of the Triangle:
The perimeter of the triangle is given as [tex]\( 7.5 \)[/tex] meters. The perimeter of any triangle is the sum of its three sides.
3. Express the Perimeter Using Side Lengths:
Since the triangle is isosceles, let's assume the two equal sides have a length of [tex]\( x \)[/tex]. We can write the equation for the perimeter as:
[tex]\[
x + x + y = 7.5
\][/tex]
Simplifying, this becomes:
[tex]\[
2x + y = 7.5
\][/tex]
4. Substitute the Known Value of [tex]\( y \)[/tex]:
We know that the shortest side [tex]\( y \)[/tex] is [tex]\( 2.1 \)[/tex] meters. Substitute this into the perimeter equation:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
Thus, the equation that can be used to find the value of [tex]\( x \)[/tex] is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
This equation correctly represents the relationship between the lengths of the sides in the isosceles triangle and its given perimeter.
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