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⋅ (o−2a)=2⋅ S  a⋅ (130−2a)=2⋅ 800.25 −2a2+130a−1600.5=0 2a2−130a+1600.5=0  p=2;q=−130;r=1600.5 D=q2−4pr=1302−4⋅2⋅1600.5=4096 D>0  a1,2​=2p−q±D​​=4130±4096​​ a1,2​=4130±64​ 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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