High School

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The isosceles triangle has a perimeter of 7.5 m. Which equation can be used to find the value of [tex]x[/tex] if the shortest side, [tex]y[/tex], measures 2.1 m?

A. [tex]2x - 2.1 = 7.5[/tex]
B. [tex]4.2 + y = 7.5[/tex]
C. [tex]y - 4.2 = 7.5[/tex]
D. [tex]2.1 + 2x = 7.5[/tex]

Answer :

To solve this problem, let's break it down step by step:

1. Understand the given information:
- We have an isosceles triangle with a perimeter of 7.5 meters.
- The shortest side, denoted as [tex]\( y \)[/tex], measures 2.1 meters.
- In an isosceles triangle, two sides are of equal length. Let’s assume those two equal sides are each [tex]\( x \)[/tex].

2. Set up the equation:
- The perimeter of a triangle is the sum of the lengths of all its sides.
- Since the triangle is isosceles with two sides equal, the equation for the perimeter can be written as:
[tex]\[
y + 2x = \text{perimeter}
\][/tex]

3. Substitute the known values:
- We know [tex]\( y = 2.1 \)[/tex] meters and the perimeter is 7.5 meters. Substitute these into the equation:
[tex]\[
2.1 + 2x = 7.5
\][/tex]

4. Select the correct option:
- This matches one of the options given: [tex]\( 2.1 + 2x = 7.5 \)[/tex].

Therefore, the equation [tex]\( 2.1 + 2x = 7.5 \)[/tex] can be used to find the value of [tex]\( x \)[/tex].

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Rewritten by : Jeany