Question

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.

Answer 1

So the triangle ABC is an isosceles triangle

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.

`AB = 6x\\AC = 4x + 6\\BC = 8x + 3`

So:

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

Now we solve for the variable x.

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

`18x + 9 = 63`

`18x = 54`

`x=(54)/(18)\\\\x=3`

Therefore:

`AB = 6(3)=18\\AC = 4(3)+6=18\\BC = 8(3) + 3=27`

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