Garden

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

Correct answer:

a =  48.5 m
b =  16.5 m

Step-by-step explanation:

o=130 m S=800.25  2a+2b = o ab = S  a⋅ (o−2a)/2=S  a⋅ (130−2a)/2=800.25 −a2+65a−800.25=0 a2−65a+800.25=0  p=1;q=−65;r=800.25 D=q2−4pr=652−4⋅1⋅800.25=1024 D>0  a1,2​=2p−q±D​​=265±1024​​ a1,2​=265±32​ a1,2​=32.5±16 a1​=48.5 a2​=16.5  a=a1​=48.5=48.5 m

Our quadratic equation calculator calculates it.

b=a2​=16.5=233​   Verifying Solution:   S2​=a⋅ b=48.5⋅ 16.5=43201​=800.25 m2 o2​=2⋅ (a+b)=2⋅ (48.5+16.5)=130 m  b=a2​=16.5=16.5 m

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