Garden fencing

Calculate the area of ​​a rectangular garden if it consumed 266 ordinary meters of mesh on its fencing and if we know that the difference between the lengths of two adjacent sides of the garden is 15 m.

Final Answer:

S =  4366 m²

Step-by-step explanation:

$$\begin{gathered} o=266\text{bm} \\ a-b=15 \\ 2(a+b)=266 \\ a-b=15 \\ 2\cdot (a+b)=266 \\ a-b=15 \\ 2a+2b=266 \\ Pivot:Row1\leftrightarrow Row2 \\ 2a+2b=266 \\ a-b=15 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ 2a+2b=266 \\ -2b=-118 \\ b=\frac{-118}{-2}=59 \\ a=\frac{266-2b}{2}=\frac{266-2\cdot 59}{2}=74 \\ a=74 \\ b=59 \\ S=a\cdot b=74\cdot 59=4366{\text{m}}^2 \end{gathered}$$

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