Rectangular garden

Divide a square garden with a perimeter of 124 m into two rectangular gardens, with the fence of one garden 10 m longer than the fence of the other. What dimensions will these rectangular gardens be?

Final Answer:

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

Step-by-step explanation:

$a=124/4=31\text{m}$

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

$d=a=31=31\text{m}$

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