Answer:
[tex]x=12[/tex]
Step-by-step explanation:
we know that
An equilateral triangle has three equal sides and three equal interior angles (each angle measures 60 degrees)
In this problem we have a equilateral triangle
so
[tex]AB=BC=AC[/tex]
Equate AB=BC
[tex](4x-10)=(3x+2)[/tex]
solve for x
[tex](4x-3x)=(10+2)[/tex]
[tex]x=12[/tex]
Verify the length of each side
[tex]AB=4x-10=4(12)-10=38\ units[/tex]
[tex]BC=3x+2=3(12)+2=38\ units[/tex]
[tex]AC=5x-22=5(12)-22=38\ units[/tex]
therefore
[tex]AB=BC=AC[/tex] ---> is correct
