Calculate Perimeter: Complex Right-Angled Shape with 5, 10, and 15 Unit Measurements

To solve this problem, we'll first examine the given shape and identify the lengths of each side along its perimeter:

• The left side is formed by three vertical segments of length 5 each, totaling $5 + 5 + 5 = 15$.
• The top horizontal side is composed of two segments: one of length 5 and another of length 10, totaling $5 + 10 = 15$.
• The bottom side is a continuous horizontal line with length 15.
• The right vertical side has a single segment of length 10.

Let's list the lengths of the outer boundary sides to compute the total perimeter:

Perimeter $P =$ Sum of all external side lengths:
$P = 15$ (left) $+ 15$ (top) $+ 15$ (bottom) $+ 10$ (right).
$P = 15 + 15 + 15 + 10$.

Therefore, the solution to the problem is $P = 55$.