Determine if Triangle ABC with Sides 2X and 12-X is Equilateral

Question

Given the size of the 3 sides of the triangle, is it an equilateral triangle?

00:00 Determine whether the triangle is equilateral

00:03 Let's treat it as equilateral, determine the value of X and then finally verify

00:07 Proceed to equate the two sides and determine X

00:11 Isolate X

00:16 This is the value of X assuming the sides are equal, let's not proceed to verify this

00:19 Substitute X into each side and check whether all the sides are equal

00:31 This is the value of one side

00:34 Substitute into the second side

00:38 The same once again for the third side, the triangle is indeed equilateral

00:41 This is the solution

To determine if the triangle is equilateral, we need to check if all three sides of the triangle are equal.

The given side lengths are $2X$ , $12 - X$ , and $12 - X$ .

For the triangle to be equilateral, we must have the equality:

Let's solve this equation:

$\begin{aligned} 2X &= 12 - X \\ 2X + X &= 12 \\ 3X &= 12 \\ X &= \frac{12}{3} \\ X &= 4 \end{aligned}$

Substitute $X = 4$ back into the expressions for the sides:

The three calculated side lengths are $8$ , $8$ , and $8$ .

Since all three sides are equal, the triangle is an equilateral triangle.

Therefore, the answer is Yes, the triangle is equilateral.

Yes