Gardens

The garden has a square shape with a circumference of 124 m. Divide it into two rectangular gardens; one should have a circumference of 10 meters more than the second. What size will the gardens be?

Final Answer:

a =  31 m
b =  18 m
c =  31 m
d =  13 m

Step-by-step explanation:

$$\begin{gathered} o=124\text{m} \\ a=o/4=124/4=31\text{m} \\ c=a=31\text{m} \\ 2(a+b)=10+2(c+d) \\ b+d=a \\ 2(31+b)=10+2(31+d) \\ b+d=31 \\ 2\cdot (31+b)=10+2\cdot (31+d) \\ b+d=31 \\ 2b-2d=10 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ 2d=26 \\ d=\frac{26}{2}=13 \\ b=\frac{10+2d}{2}=\frac{10+2\cdot 13}{2}=18 \\ b=18 \\ d=13 \end{gathered}$$

$$\begin{gathered} d=13=13\text{m} \\ \text{ Verifying Solution: } \\ {o}_1=2\cdot (a+b)=2\cdot (31+18)=98\text{m} \\ {o}_2=2\cdot (c+d)=2\cdot (31+13)=88\text{m} \end{gathered}$$

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