Question

question 3: determine the perimeter of the triangle.

Explanation:

Step1: Identify the type of triangle

The triangle is equilateral (all sides equal).

Step2: Recall the formula for perimeter of an equilateral triangle

Perimeter \(P = 3\times\) side length. Given side length \(s=12\sqrt{18x^{2}}\).
First simplify \(12\sqrt{18x^{2}}\):
\(\sqrt{18x^{2}}=\sqrt{9\times2\times x^{2}} = 3x\sqrt{2}\), so \(12\sqrt{18x^{2}}=12\times3x\sqrt{2}=36x\sqrt{2}\).

Step3: Calculate the perimeter

\(P = 3\times36x\sqrt{2}\)
\(P=108x\sqrt{2}\)

Answer:

\(108x\sqrt{2}\)