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.

Correct result:

a =  225 m
b =  75 m

Solution:

o=600 m S=16875 m2  S=ab o=2(a+b)=2a+2b  16875=a(600/2a)  16875=a (600/2a) a2300a+16875=0  p=1;q=300;r=16875 D=q24pr=30024116875=22500 D>0  a1,2=q±D2p=300±225002 a1,2=300±1502 a1,2=150±75 a1=225 a2=75   Factored form of the equation:  (a225)(a75)=0  a=a1=225 mo=600 \ \text{m} \ \\ S=16875 \ \text{m}^2 \ \\ \ \\ S=ab \ \\ o=2(a+b)=2a+2b \ \\ \ \\ 16875=a*(600/2-a) \ \\ \ \\ 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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