3. ALGEBRA Find $$ x $$ and the length of each side if $$ riangle W X Y $$ is an equilateral triangle with sides $$ \overline{W X}=6 x-12, \overline{X Y}=2 x+10 $$, and $$ \overline{W Y}=4 x-1 $$.

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3. ALGEBRA Find $$ x $$ and the length of each side if $$ 	riangle W X Y $$ is an equilateral triangle with sides $$ \overline{W X}=6 x-12, \overline{X Y}=2 x+10 $$, and $$ \overline{W Y}=4 x-1 $$.

UpStudy AI · Accepted Answer

To solve for $$ x $$ and determine the length of each side of the equilateral triangle $$ \triangle WXY $$, we'll use the fact that all sides of an equilateral triangle are equal.

Given:
- $$ \overline{WX} = 6x - 12 $$
- $$ \overline{XY} = 2x + 10 $$
- $$ \overline{WY} = 4x - 1 $$

Since all sides are equal:
$$ 6x - 12 = 2x + 10 $$
$$ 6x - 12 = 4x - 1 $$
$$ 2x + 10 = 4x - 1 $$

Let's solve the first equation:
$$ 6x - 12 = 2x + 10 $$
Subtract $$ 2x $$ from both sides:
$$ 4x - 12 = 10 $$
Add $$ 12 $$ to both sides:
$$ 4x = 22 $$
Divide by $$ 4 $$:
$$ x = \frac{22}{4} = 5.5 $$

Now, substitute $$ x = 5.5 $$ back into any of the side expressions to find the length of each side:
$$ \overline{WX} = 6(5.5) - 12 = 33 - 12 = 21 $$
$$ \overline{XY} = 2(5.5) + 10 = 11 + 10 = 21 $$
$$ \overline{WY} = 4(5.5) - 1 = 22 - 1 = 21 $$

**Answer:**
The value of $$ x $$ is 5.5, and each side of the equilateral triangle measures 21 units.
$$ x = 5.5 $$ and each side of the triangle is 21 units long.

ALGEBRA Find and the length of each side if is an equilateral triangle with sides
, and .

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