144 steps

To get around the garden, we have to take 144 steps—eight steps less in width than in length. One step is five decimetres long. What are the dimensions of the garden? What are its perimeter and its area?

Final Answer:

a =  20 m
b =  16 m
o =  72 m
S =  320 m²

Step-by-step explanation:

$$\begin{gathered} k=5\text{dm}\to \text{m}=5:10\text{m}=0.5\text{m} \\ o=144\cdot k=144\cdot 0.5=72\text{m} \\ 2\cdot (a+b)=o \\ a=b+8\cdot k \\ 2\cdot (a+b)=72 \\ a=b+8\cdot 0.5 \\ 2a+2b=72 \\ a-b=4 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ -2b=-32 \\ b=\frac{-32}{-2}=16 \\ a=\frac{72-2b}{2}=\frac{72-2\cdot 16}{2}=20 \\ a=20 \\ b=16 \end{gathered}$$

$S=a\cdot b=20\cdot 16=320{\text{m}}^2$

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