Answer:
29.0 m
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4cm}\underline{Area of a semicircle}\\\\$A=\dfrac{1}{2}\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius\\ \end{minipage}}[/tex]
Given the area of the semicircle is 50 m², substitute this into the formula and rearrange to isolate r:
[tex]\begin{aligned}\implies\dfrac{1}{2}\pi r^2&=50\\\pi r^2 & = 100\\r^2 & = \dfrac{100}{\pi}\\r&=\sqrt{\dfrac{100}{\pi}}\end{aligned}[/tex]
The perimeter of a semicircle is the sum of the diameter of the circle and half its circumference.
- Diameter of a circle = 2r
- Circumference of a circle = 2πr
Therefore:
[tex]\begin{aligned}\textsf{Perimeter of a semicircle}&=2r+\pi r\\&=r(2+\pi)\\&=\sqrt{\dfrac{100}{\pi}}(2+\pi)\\&=29.0083301...\end{aligned}[/tex]
Therefore, the perimeter of the semicircle is 29.0 m (1 d.p.).
