Equilateral Triangle Verification: Comparing Sides 10+X, 5X-10, and 3X

Question

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

00:13 Let's check if the triangle is equilateral.

00:17 Assume it's equilateral, find X, then verify.

00:22 Set the two sides equal and find X.

00:26 Isolate the variable X.

00:28 This is X, assuming sides are equal. Let's verify!

00:33 Plug in X to each side and check if all sides match.

00:44 Here's the length of one side.

00:49 Substitute in the second side; same result!

00:53 The third side matches too. It's equilateral!

00:58 And that's the solution!

To determine if the given triangle is equilateral, we need to ensure that all sides are equal. Given the sides:

Since two sides are already equal ( $a = b$ ), we need to check if this is equal to the third side:

Set the side lengths $a$ and $c$ equal:

$10 + X = 5X - 10$

Solve for $X$ :

$10 + X = 5X - 10$

Subtract $X$ from both sides:

$10 = 4X - 10$

Add 10 to both sides:

$20 = 4X$

Divide by 4:

$X = 5$

Substitute $X = 5$ back into the side length expressions:

All sides are equal to 15. Hence, the triangle is equilateral.

Therefore, the solution to the problem is Yes.

Yes