Given equilateral \(\triangle XYZ\), find the values of x and y.

Side lengths:
- XY = 12
- XZ = 3x - 2
- YZ = \(\frac{1}{3}y + 1\)

In equilateral triangle △ X Y Z , the value of x is 3 14 ​ and the value of y is 33 . Both values were found by setting the side lengths equal and solving the resulting equations. This demonstrates the properties of equilateral triangles where all sides are equal.
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Answered by Anonymous | 2025-07-04

To find the values of x and y for the equilateral triangle △ X Y Z , we know the following:

In an equilateral triangle, all sides are equal in length.

Therefore, we have the following equations based on the given side lengths:

X Y = XZ = Y Z = 12

Given:

X Y = 12
XZ = 3 x − 2
Y Z = 3 1 ​ y + 1


Since all sides are equal, we set up the equations:

3 x − 2 = 12
3 1 ​ y + 1 = 12


Solving for x :

3 x − 2 = 12
Add 2 to both sides: 3 x = 14
Divide by 3: x = 3 14 ​ ≈ 4.67


Solving for y :

3 1 ​ y + 1 = 12
Subtract 1 from both sides: 3 1 ​ y = 11
Multiply by 3: y = 33



Therefore, the values of x and y are x = 3 14 ​ and y = 33 , respectively. These solutions ensure that the triangle remains equilateral, as all sides are equal to 12.

Answered by MasonWilliamTurner | 2025-07-06