# Rectangular garden 2

A farmer bought 600 m of wire for the fence. He wants to use it to besiege a rectangular garden with a surface of 16875 m2. Calculate the size of the garden.

Result

a =  225 m
b =  75 m

#### Solution:

$o=600 \ \text{m} \ \\ S=16875 \ \text{m}^2 \ \\ \ \\ S=ab \ \\ o=2(a+b)=2a+2b \ \\ \ \\ \ \\ 16875=a \cdot \ (600/2-a) \ \\ a^2 -300a +16875=0 \ \\ \ \\ p=1; q=-300; r=16875 \ \\ D=q^2 - 4pr=300^2 - 4\cdot 1 \cdot 16875=22500 \ \\ D>0 \ \\ \ \\ a_{1,2}=\dfrac{ -q \pm \sqrt{ D } }{ 2p }=\dfrac{ 300 \pm \sqrt{ 22500 } }{ 2 } \ \\ a_{1,2}=\dfrac{ 300 \pm 150 }{ 2 } \ \\ a_{1,2}=150 \pm 75 \ \\ a_{1}=225 \ \\ a_{2}=75 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (a -225) (a -75)=0 \ \\ \ \\ a=a_{1}=225 \ \text{m}$

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$b=o/2-a=600/2-225=75 \ \\ b=a_{2}=75 \ \text{m}$

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