Park path triangle

The paths in the park form a right-angled triangle, which on the map with a scale of 1:200 has two dimensions of side lengths of 9 cm and 15 cm. Grandma walks this route every day for a health walk. How many meters does she walk?

Final Answer:

S =  270 m²
n =  7

Step-by-step explanation:

$$\begin{gathered} a=9\text{cm}\to \text{m}=9:100\text{m}=0.09\text{m} \\ b=15\text{cm}\to \text{m}=15:100\text{m}=0.15\text{m} \\ M=200 \\ A=M\cdot a=200\cdot 0.09=18\text{m} \\ B=M\cdot b=200\cdot 0.15=30\text{m} \\ C=\sqrt{A^2+B^2}=\sqrt{18^2+30^2}=6\sqrt{34}\text{m}\doteq 34.9857\text{m} \\ S=\frac{A\cdot B}{2}=\frac{18\cdot 30}{2}=270{\text{m}}^2 \end{gathered}$$

$$\begin{gathered} o=A+B+C=18+30+34.9857\doteq 82.9857\text{m} \\ s=0.5\text{km}\to \text{m}=0.5\cdot 1000\text{m}=500\text{m} \\ {n}_1=s/o=500/82.9857\doteq 6.0251 \\ n=\lceil n_1\rceil =\lceil 6.0251\rceil =7 \end{gathered}$$

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