Question

determine the expression that represents the perimeter of the given composite figure. (figure is not drawn to scale)

Explanation:

Step1: Identify all side - lengths

The side - lengths of the composite figure are \(12x\), \(6x\), \(4x\) and some other sides which can be deduced from the right - angled nature of the figure. The vertical side on the left is \(6x + ( \text{the vertical part of the lower right section})\). Since the figure is composed of right - angled shapes, we can find all the outer side - lengths. The outer side - lengths are \(12x\), \(6x\), \(4x\), and by symmetry and right - angles, the other side - lengths are also part of the perimeter.

Step2: Sum up all side - lengths

The perimeter \(P\) of a polygon is the sum of all its outer side - lengths.

$$P=12x + 6x+4x + 12x+6x + 4x$$

$$P=(12 + 6+4 + 12+6 + 4)x$$

$$P = 44x$$

Answer:

\(44x\)