Question

1. precision is the triangle an equilateral triangle? justify your answer. 2x + 5.2, 3x + 1.2, 2x + 6.2 section 1.3 solving equations with variables on both sides

Explanation:

Step1: Set two sides equal (find x)

For a triangle to be equilateral, all sides must be equal. First, set \(2x + 5.2\) equal to \(3x + 1.2\) (two of the sides).
\(2x + 5.2 = 3x + 1.2\)
Subtract \(2x\) from both sides: \(5.2 = x + 1.2\)
Subtract \(1.2\) from both sides: \(x = 4\)

Step2: Calculate each side's length

Now substitute \(x = 4\) into each side's expression:

• First side: \(2x + 5.2 = 2(4) + 5.2 = 8 + 5.2 = 13.2\)
• Second side: \(3x + 1.2 = 3(4) + 1.2 = 12 + 1.2 = 13.2\)
• Third side: \(2x + 6.2 = 2(4) + 6.2 = 8 + 6.2 = 14.2\)

Step3: Check if all sides are equal

Compare the three lengths: \(13.2\), \(13.2\), and \(14.2\). Since \(14.2
eq 13.2\), not all sides are equal.

Answer:

No, the triangle is not equilateral. When solving for \(x\) (by setting two sides equal), we find \(x = 4\). Substituting \(x = 4\) into each side’s expression gives side lengths \(13.2\), \(13.2\), and \(14.2\), which are not all equal.