classify triangle ABC by its sides if side AB=6x, side AC=4x+6 and side BC=8x+3. the perimeter of triangle ABC is 63.

To classify triangle ABC by its sides, we need to determine if it is an equilateral triangle, an isosceles triangle, or a scalene triangle.

1. Let's start by finding the value of x. We know that the perimeter of triangle ABC is given by the sum of the lengths of its three sides. So we can set up an equation:

Perimeter = AB + AC + BC

63 = 6x + (4x + 6) + (8x + 3)

2. Simplify the equation:

63 = 6x + 4x + 6 + 8x + 3

Combine like terms:

63 = 18x + 9

3. Subtract 9 from both sides of the equation:

63 - 9 = 18x + 9 - 9

54 = 18x

4. Divide both sides of the equation by 18:

54/18 = 18x/18

3 = x

Now we know that x = 3.

5. Substitute the value of x back into the expressions for the sides:

AB = 6x = 6(3) = 18
AC = 4x + 6 = 4(3) + 6 = 12 + 6 = 18
BC = 8x + 3 = 8(3) + 3 = 24 + 3 = 27

The lengths of the sides of triangle ABC are: AB = 18, AC = 18, and BC = 27.

6. Classify the triangle based on the lengths of its sides:

Since all three sides have different lengths (AB ≠ AC ≠ BC), triangle ABC is classified as a scalene triangle.