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Mathematics-Online problems:

Interactive Problem 173: Restructuring of an Area and Shares of Costs

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Having become insolvent, a company is liquidated and its property in need of rehabilitation is transferred to the four municipalities $ A$, $ B$, $ C$, and $ D$ neighboring these premises. The municipalities decide to divide up and restructure a quadratic area of 1km$ ^2$ altogether (left drawing), which encloses the premises in need of rehabilitation (shaded square). After restructuring the area, the borders should be straight lines (right drawing).

The clean-up costs totalling 9 million Euro are to be divided among the municipalities according to the parts of the premises they obtain. Since the municipalities $ A$ and $ B$ are not able to bear any clean-up costs due to their deplorable financial situation, the size of their part of the whole area should stay unchanged.

\includegraphics[width=0.5\linewidth]{TdM_09_A2_bild1.eps}

Determine the areas of all estates before and after restructuring, the lengths of the new borderlines, and the shares of the clean-up costs the two municipalities incurred.


Answer:

Areas:
$ A:$          $ B:$
$ C:$          $ C':$
$ D:$          $ D':$
(Areas in square meters)

Lengths of borderlines:
$ \,\,x:$          $ \,\,\,y:$

Clean-up costs:
$ \,$Share of $ C:$      $ \,$Share of $ D:$
(Amounts in euros)


   

(From: Mathematics Contest 2009)
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  automatically generated: 8/11/2017