Park

In the park is a marked diamond-shaped line connecting locations A, D, S, C, B, and A. Calculate its length if |AB| = 108 m, |AC| = 172.8 m.

Final Answer:

x =  475.2 m

Step-by-step explanation:

$$\begin{gathered} a=108\text{m} \\ {d}_1=172.8\text{m} \\ {a}^2=(d_1/2{)}^2+(d_2/2{)}^2 \\ 4a^2=d_1^2+d_2^2 \\ {d}_2^2=4a^2-d_1^2 \\ {d}_2=\sqrt{4\cdot a^2-d_1^2}=\sqrt{4\cdot 108^2-172.8^2}=\frac{648}{5}=129.6\text{m} \\ x=3\cdot a+d_1/2+d_2/2=3\cdot 108+172.8/2+129.6/2=475.2\text{m} \end{gathered}$$

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