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 answer:

a =  225 m
b =  75 m

Step-by-step explanation:

$$\begin{gathered} o=600\text{m} \\ S=16875{\text{m}}^2 \\ S=ab \\ o=2(a+b)=2a+2b \\ 16875=a\cdot (600/2-a) \\ 16875=a\cdot (600/2-a) \\ {a}^2-300a+16875=0 \\ p=1;q=-300;r=16875 \\ D=q^2-4pr=300^2-4\cdot 1\cdot 16875=22500 \\ D>0 \\ {a}_{1,2}=\frac{-q\pm \sqrt{D}}{2p}=\frac{300\pm \sqrt{22500}}{2} \\ {a}_{1,2}=\frac{300\pm 150}{2} \\ {a}_{1,2}=150\pm 75 \\ {a}_1=225 \\ {a}_2=75 \\ a=a_1=225=225\text{m} \end{gathered}$$

Our quadratic equation calculator calculates it.

$$\begin{gathered} b=o/2-a=600/2-225=75=75\text{m} \\ b=a_2 \end{gathered}$$

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