Garden

The garden has a rectangular shape and has a circumference of 130 m and area 800.25 m2. Calculate the dimensions of the garden.

Result

a =  48.5 m
b =  16.5 m

Solution:

2a+2b=130 ab=800.25  a(1302a)/2=800.25  a(65a)=800.25 a265a+800.25=0 a1,2=q±D2p=65±10242 a1,2=65±322 a1,2=32.5±16 a1=48.5 a2=16.5 a=48.5 m2a+2b = 130 \ \\ ab = 800.25 \ \\ \ \\ a(130-2a)/2=800.25 \ \\ \ \\ a(65-a)=800.25 \ \\ a^2 -65a + 800.25 = 0 \ \\ a_{1,2} = \dfrac{ -q \pm \sqrt{ D } }{ 2p } = \dfrac{ 65 \pm \sqrt{ 1024 } }{ 2 } \ \\ a_{1,2} = \dfrac{ 65 \pm 32 }{ 2 } \ \\ a_{1,2} = 32.5 \pm 16 \ \\ a_{1} = 48.5 \ \\ a_{2} = 16.5 \ \\ a = 48.5 \ \text{m}
b=16.5 mb=16.5 \ \text{m}



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