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. Show all your work. Explain your reasoning.

Just add up the sides and solve for x:

6x + 4x+6 + 8x+3 = 63
18x + 9 = 63
18x = 54
x = 3

sides are 18,18,26

so it's isoceles

To classify triangle ABC by its sides, we need to compare the lengths of its three sides.

Given that side AB = 6x, side AC = 4x + 6, and side BC = 8x + 3, we can set up an equation to find the value of x.

Perimeter of a triangle is the sum of all its sides. In this case, the perimeter is given as 63. Therefore, we can write the equation:

AB + AC + BC = 63

Replacing the given values:

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

Combine like terms:

18x + 9 = 63

Subtracting 9 from both sides:

18x = 54

Dividing both sides by 18:

x = 3

Now that we have the value of x, we can substitute it back into the original expressions for the sides to find their actual lengths:

AB = 6x = 6 * 3 = 18
AC = 4x + 6 = 4 * 3 + 6 = 18
BC = 8x + 3 = 8 * 3 + 3 = 27

By comparing the lengths of the sides, we can classify the triangle:

Since all three sides are different lengths, it is a scalene triangle.