Question
Find the values of \( x \) and \( y i f \) the sides of an equilateral triangle are \( 4,2 x \) and \( 2 y-1 \). \( x=4, y=2 \) \( x=4, y=2.5 \) \( x=2, y=2.5 \) \( x=2, y=3 \)
Ask by Nichols Mcguire. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = 2 \) and \( y = 2.5 \)
Solution
Since the triangle is equilateral, all its sides must be equal. The sides are given as:
Side 1: 4
Side 2: 2x
Side 3: 2y - 1
Setting the sides equal to each other:
1. Equate Side 1 and Side 2:
4 = 2x
x = 4/2 = 2
2. Equate Side 1 and Side 3:
4 = 2y - 1
2y = 4 + 1 = 5
y = 5/2 = 2.5
Thus, the values are x = 2 and y = 2.5, which corresponds to the third option.
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Simplify this solution Extra Insights
In an equilateral triangle, all sides must be equal. Since we have the sides \( 4, 2x, \) and \( 2y - 1 \), we can set up the following equations based on their equality: 1. \( 4 = 2x \) 2. \( 4 = 2y - 1 \) 3. \( 2x = 2y - 1 \) Solving the first equation: \[ 2x = 4 \Rightarrow x = 2. \] For the second equation: \[ 2y - 1 = 4 \Rightarrow 2y = 5 \Rightarrow y = 2.5. \] Thus, the values are \( x = 2 \) and \( y = 2.5 \). The correct choice from your options is \( x=2, y=2.5 \).
