Rectangular 6255

The lengths of the sides of the rectangular garden are in the ratio of 1: 2. The connection of the centers of the adjacent sides is 20 m long. Calculate the perimeter and area of the rectangle.

Correct answer:

o =  107.3313 m
S =  640 m²

Step-by-step explanation:

$$\begin{gathered} a:b=1:2 \\ b=2a \\ 20^2=(a/2{)}^2+(b/2{)}^2=(17.8885/2{)}^2+(35.7771/2{)}^2=0 \\ 20^2=(a/2{)}^2+(2a/2{)}^2 \\ -1.25a^2+400=0 \\ 1.25a^2-400=0 \\ p=1.25;q=0;r=-400 \\ D=q^2-4pr=0^2-4\cdot 1.25\cdot (-400)=2000 \\ D>0 \\ {a}_{1,2}=\frac{-q\pm \sqrt{D}}{2p}=\frac{\pm \sqrt{2000}}{2.5}=\frac{\pm 20\sqrt{5}}{2.5} \\ {a}_{1,2}=\pm 8\sqrt{5}=\pm 17.888543819998 \\ {a}_1=8\sqrt{5}=17.888543819998 \\ {a}_2=-8\sqrt{5}=-17.888543819998 \\ \text{ Factored form of the equation: } \\ 1.25(a-17.888543819998)(a+17.888543819998)=0 \\ a>0 \\ a=a_1=17.8885=8\sqrt{5}\text{m}\doteq 17.8885\text{m} \\ b=2\cdot a=2\cdot 17.8885=16\sqrt{5}\text{m}\doteq 35.7771\text{m} \\ o=2\cdot (a+b)=2\cdot (17.8885+35.7771)=48\sqrt{5}=107.3313\text{m} \end{gathered}$$

Our quadratic equation calculator calculates it.

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

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