Answer:
So the triangle ABC is an isosceles triangle
Step-by-step explanation:
By definition the perimeter of a triangle is equal to the sum of the lengths of its sides.
In this case we know that the perimeter is 63
The lengths of its sides depend on x.
[tex]AB = 6x\\AC = 4x + 6\\BC = 8x + 3[/tex]
So:
[tex]6x + 4x + 6 + 8x + 3 = 63[/tex]
Now we solve for the variable x.
[tex]6x + 4x + 6 + 8x + 3 = 63[/tex]
[tex]18x + 9 = 63[/tex]
[tex]18x = 54[/tex]
[tex]x=\frac{54}{18}\\\\x=3[/tex]
Therefore:
[tex]AB = 6(3)=18\\AC = 4(3)+6=18\\BC = 8(3) + 3=27[/tex]
The triangle has two sides of equal length. The triangles that have two equal sides are the isosceles triangles.
So the triangle ABC is an isosceles triangle
