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Answer :
To solve the problem of finding the value of [tex]\( x \)[/tex] for the isosceles triangle with a perimeter of 7.5 meters and the shortest side [tex]\( y \)[/tex] measuring 2.1 meters, we need to first understand the properties of an isosceles triangle.
In an isosceles triangle, two sides are equal in length. Let's assume these two equal sides have a length represented by [tex]\( x \)[/tex]. The perimeter of the triangle is the sum of all its sides. Therefore, we can set up the equation for the perimeter as:
[tex]\[ y + 2x = 7.5 \][/tex]
We know that the shortest side [tex]\( y \)[/tex] is 2.1 meters. Substituting this into the equation gives us:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
This is the equation we can use to find the value of [tex]\( x \)[/tex].
To solve for [tex]\( x \)[/tex], follow these steps:
1. Subtract 2.1 from both sides of the equation:
[tex]\[ 2x = 7.5 - 2.1 \][/tex]
[tex]\[ 2x = 5.4 \][/tex]
2. Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{5.4}{2} \][/tex]
[tex]\[ x = 2.7 \][/tex]
Therefore, the equation that can be used to find the value of [tex]\( x \)[/tex] is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
And the value of [tex]\( x \)[/tex] is 2.7 meters.
In an isosceles triangle, two sides are equal in length. Let's assume these two equal sides have a length represented by [tex]\( x \)[/tex]. The perimeter of the triangle is the sum of all its sides. Therefore, we can set up the equation for the perimeter as:
[tex]\[ y + 2x = 7.5 \][/tex]
We know that the shortest side [tex]\( y \)[/tex] is 2.1 meters. Substituting this into the equation gives us:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
This is the equation we can use to find the value of [tex]\( x \)[/tex].
To solve for [tex]\( x \)[/tex], follow these steps:
1. Subtract 2.1 from both sides of the equation:
[tex]\[ 2x = 7.5 - 2.1 \][/tex]
[tex]\[ 2x = 5.4 \][/tex]
2. Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{5.4}{2} \][/tex]
[tex]\[ x = 2.7 \][/tex]
Therefore, the equation that can be used to find the value of [tex]\( x \)[/tex] is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
And the value of [tex]\( x \)[/tex] is 2.7 meters.
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