Area of garden

If the width of the rectangular garden is decreased by 2 meters and its length is increased by 5 meters, the area of the rectangle will be 0.2 ares larger. If the width and the length of the garden will increase by 3 meters, its original size will increase by 0.9 ares. Find the dimensions of the garden.

Correct answer:

a =  12 m
b =  15 m

Step-by-step explanation:

$$\begin{gathered} (a-2)\cdot (b+5)=ab+0.2\cdot 100 \\ (a+3)\cdot (b+3)=ab+0.9\cdot 100 \\ 5a-2b=30 \\ a+b=27 \\ 5\cdot a-2\cdot b=30 \\ a+b=27 \\ 5a-2b=30 \\ a+b=27 \\ Row2-\frac{1}{5}\cdot Row1\to Row2 \\ 5a-2b=30 \\ 1.4b=21 \\ b=\frac{21}{1.4}=15 \\ a=\frac{30+2b}{5}=\frac{30+2\cdot 15}{5}=12=12\text{m} \\ a=12 \\ b=15 \end{gathered}$$

$b=15=15\text{m}$

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