Garden dimensions

The lengths of the sides of the rectangular garden are in the ratio of 1:2. The junction of the centers of adjacent sides is 20 m long. Calculate the perimeter and acreage of the land.

Final Answer:

o =  107.3313 m
S =  640 m²

Step-by-step explanation:

$$\begin{gathered} a:b=1:2 \\ 2a=b \\ (a/2{)}^2+(b/2{)}^2=20^2 \\ (a/2{)}^2+(2a/2{)}^2=20^2 \\ {a}^2+4a^2=20^2\cdot 4 \\ a=\sqrt{20^2\cdot 4/(1+4)}=8\sqrt{5}\doteq 17.8885 \\ b=2\cdot a=2\cdot 17.8885=16\sqrt{5}\doteq 35.7771 \\ o=2\cdot (a+b)=2\cdot (17.8885+35.7771)=48\sqrt{5}\doteq 107.3313\text{m} \\ k=1/2\cdot \sqrt{a^2+b^2}=1/2\cdot \sqrt{17.8885^2+35.7771^2}=20 \end{gathered}$$

$S=a\cdot b=17.8885\cdot 35.7771=640{\text{m}}^2$

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