Answer:
[tex]x=9, AB=BC=AC=35[/tex]
Step-by-step explanation:
Equilateral triangles have 3 congruent sides, so all 3 sides have the same length. Therefore, we know that [tex]AB=BC=AC[/tex]. We are given the lengths of all 3 sides in terms of [tex]x[/tex], but we only need to set two of them equal to each other to solve for [tex]x[/tex]. Let's use [tex]AB[/tex] and [tex]BC[/tex] to solve for [tex]x[/tex]. We know that [tex]AB=BC[/tex], [tex]AB=2x+17[/tex], and [tex]BC=6x-19[/tex]. Therefore, we can write the following equation to solve for
[tex]AB=BC\\2x+17=6x-19[/tex] (Substitute given values into equation)
Solving for [tex]x[/tex], we get:
[tex]2x+17=6x-19\\2x+17-17=6x-19-17[/tex] (Subtract [tex]17[/tex] from both sides of the equation to isolate constants)
[tex]2x=6x-36[/tex] (Simplify)
[tex]2x-6x=6x-36-6x[/tex] (Subtract [tex]6x[/tex] from both sides of the equation to isolate [tex]x[/tex])
[tex]-4x=-36[/tex] (Simplify)
[tex]\frac{-4x}{-4}=\frac{-36}{-4}[/tex] (Divide both sides of the equation by [tex]-4[/tex] to get rid of [tex]x[/tex]'s coefficient)
[tex]x=9[/tex] (Simplify)
Therefore, [tex]AB=2x+17=2*9+17=18+17=35[/tex], and [tex]AB=BC=AC=35[/tex]. Hope this helps!
