Rectangular garden

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

Result

S =  160 m2
o =  53.666 m

Solution:

a=1x b=2x u=20 m  u=a2+b2 u=x2+4x2=5x2 5x2=202 x=202/5=4 5 m≐8.9443 m  a=x=8.9443=4 5 m≐8.9443 m b=2⋅ x=2⋅ 8.9443=8 5 m≐17.8885 m S=a⋅ b=8.9443⋅ 17.8885=160=160 m2a = 1x \ \\ b = 2x \ \\ u = 20 \ 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 } \ m \doteq 8.9443 \ m \ \\ \ \\ a = x = 8.9443 = 4 \ \sqrt{ 5 } \ m \doteq 8.9443 \ m \ \\ b = 2 \cdot \ x = 2 \cdot \ 8.9443 = 8 \ \sqrt{ 5 } \ m \doteq 17.8885 \ m \ \\ S = a \cdot \ b = 8.9443 \cdot \ 17.8885 = 160 = 160 \ m^2
o=2⋅ (a+b)=2⋅ (8.9443+17.8885)=24 5≐53.6656=53.666  m o = 2 \cdot \ (a+b) = 2 \cdot \ (8.9443+17.8885) = 24 \ \sqrt{ 5 } \doteq 53.6656 = 53.666 \ \text{ m }

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