Triangle Side Analysis: Is 19+X = 7X+1 = 25-X an Equilateral Triangle?

Video Solution

Solution Steps

00:10 Let's check if the triangle is equilateral.

00:13 Assume the triangle is equilateral. First, we'll find the value of X. Then, we'll verify it.

00:19 Set the two sides equal to find X.

00:23 Now, solve for X. Isolate X on one side of the equation.

00:37 This is X when the sides are equal. Let's verify this assumption.

00:42 Substitute X back into each side. Check if all the sides are equal.

00:48 Here's the value of one side with X substituted in.

00:52 Now, substitute X into the second side.

00:56 Do the same for the third side. Yes, the triangle is equilateral!

01:01 And that's how we solve the problem. Great job!

Step-by-Step Solution

To solve this problem, we will follow these steps:

Step 1: Calculate when $19 + X = 7X + 1$ .
Step 2: Calculate when $7X + 1 = 25 - X$ .
Step 3: Calculate when $25 - X = 19 + X$ .
Step 4: Check that these conditions are satisfied simultaneously for the triangle to be equilateral.

Step 1: Solve $19 + X = 7X + 1$ .

Rearranging terms, we get $19 - 1 = 7X - X$ .

This simplifies to $18 = 6X$ , giving $X = 3$ .

Step 2: Solve $7X + 1 = 25 - X$ .

Rearranging terms, we get $7X + X = 25 - 1$ .

This simplifies to $8X = 24$ , giving $X = 3$ .

Step 3: Solve $25 - X = 19 + X$ .

Rearranging terms, we get $25 - 19 = X + X$ .

This simplifies to $6 = 2X$ , giving $X = 3$ .

We find that all conditions are satisfied when $X = 3$ , and thus all sides are equal at this value.

The side lengths with $X = 3$ are:

All sides become equal with $X = 3$ , thus the triangle is equilateral.

The solution to the problem is Yes.