Z6–I–2

Mr. Kockorád owned a rectangular-shaped garden, on which he gradually paved paths from one side to the other. The paths were equally wide, crossed each other at two places, and the already paved area was skipped when paving further.

When Mr. Kockorád paved a path parallel to the longer side, he used up 228 m² of paving. Then he paved a path parallel to the shorter side and used up 117 m² of paving. Finally, he paved one more path parallel to the first path, this time using up only 219 m² of paving.

Determine the dimensions of Kockorád's garden.

Final Answer:

a =  42 m
b =  76 m

Step-by-step explanation:

$$\begin{gathered} 228=b_x \\ 117=(a-x)x=a_x-x^2 \\ 219=(b-x)x=b_x-x^2 \\ 219=228-x^2 \\ {x}^2=9 \\ x=\sqrt{9}=3 \\ b=228/x=228/3=76 \\ a=(117+x^2)/x=(117+3^2)/3=42\text{m} \end{gathered}$$

$$\begin{gathered} S=a\cdot b=42\cdot 76=3192 \\ b=76=76\text{m} \end{gathered}$$

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