Rectangular garden

The sides of the rectangular garden are in a ratio of 1:2. The diagonal has a length of 20 meters. Calculate the area and perimeter of the garden.

Correct answer:

S =  160 m²
o =  53.6656 m

Step-by-step explanation:

$$\begin{gathered} a=1x \\ b=2x \\ u=20\text{m} \\ u=\sqrt{a^2+b^2} \\ u=\sqrt{x^2+4x^2}=\sqrt{5x^2} \\ 5x^2=20^2 \\ x=\sqrt{20^2/5}=4\sqrt{5}\text{m}\doteq 8.9443\text{m} \\ a=x=8.9443=4\sqrt{5}\text{m}\doteq 8.9443\text{m} \\ b=2\cdot x=2\cdot 8.9443=8\sqrt{5}\text{m}\doteq 17.8885\text{m} \\ S=a\cdot b=8.9443\cdot 17.8885=160{\text{m}}^2 \end{gathered}$$

$o=2\cdot (a+b)=2\cdot (8.9443+17.8885)=24\sqrt{5}=53.6656\text{m}$

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