1. **Problem statement:** Calculate the perimeter of the figure in problem 16, which consists of three semicircles placed horizontally. The largest semicircle has a diameter of 20 cm, and inside it are two smaller semicircles side-by-side whose diameters sum to 20 cm. 2. **Formula and rules:** The perimeter of a semicircle is half the circumference of a full circle plus the diameter (if the diameter is part of the perimeter). Here, the figure's perimeter is the sum of the outer arcs only, since the diameters inside are not part of the outer perimeter. The circumference of a circle is given by $$C = \pi d$$ where $d$ is the diameter. 3. **Step-by-step solution:** - The largest semicircle has diameter $d = 20$ cm. - The two smaller semicircles have diameters $d_1$ and $d_2$ such that $d_1 + d_2 = 20$ cm. - The perimeter consists of the arc of the largest semicircle plus the arcs of the two smaller semicircles (since the diameters inside are not on the perimeter, only the arcs count). - The length of a semicircle arc is half the circumference: $$\frac{\pi d}{2}$$ - Therefore, the total perimeter $P$ is: $$ P = \frac{\pi \times 20}{2} + \frac{\pi d_1}{2} + \frac{\pi d_2}{2} $$ - Since $d_1 + d_2 = 20$, substitute: $$ P = 10\pi + \frac{\pi d_1}{2} + \frac{\pi (20 - d_1)}{2} = 10\pi + \frac{\pi d_1}{2} + 10\pi - \frac{\pi d_1}{2} $$ - Notice $\frac{\pi d_1}{2}$ and $-\frac{\pi d_1}{2}$ cancel out: $$ P = 10\pi + 10\pi = 20\pi $$ 4. **Final answer:** $$ \boxed{20\pi \text{ cm} \approx 62.83 \text{ cm}} $$ This is the perimeter of the figure in problem 16.