Frank owns an entire city block, which is a perfectly square piece of land. One corner of the block is at the intersection of Slauson Ave. and Carmelita. Due to development in the area, the city of Huntington Park wants to widen Slauson Ave. by 3 feet by shrinking Frank's block. However, the city offers to compensate Frank by adding 3 feet to the Carmelita side of his property. Is this a fair deal?

So originally, let's say the width of Frank's land was x feet.
The area of his land was therefore x × x , or x 2 , as his land was square.
The width of his land then increased by 3 feet, and the height decreased by 3 feet.
So the new area of Frank's land is:
( x + 3 ) ( x − 3 ) = x 2 + 3 x − 3 x − 9 = x 2 − 9
So the new land is now 9 square feet smaller , so it is not a fair deal for Frank.
Hope this helps :)

Answered by ollieboyne | 2024-06-10

The city's offer to Frank is not a fair deal area-wise, as removing and adding 3 feet on perpendicular sides of a square block leads to a decrease in the total area of the property. The change might also affect property value, which could be a consideration for Frank.
When considering whether the city's offer is a fair deal for Frank as they widen Slauson Ave and compensate by adding the same width on Carmelita, it boils down to the area of his square block. If Frank's block is perfectly square, taking away 3 feet from one side and adding 3 feet to the perpendicular side does not yield an equal trade in terms of area. For example, if the block is 100 feet by 100 feet, originally the area is 10,000 square feet. Removing 3 feet from one side would make it 97 feet by 100 feet, or 9,700 square feet. Adding 3 feet to the other side would give a new dimension of 97 feet by 103 feet, or an area of 9,991 square feet. This indicates a loss of 9 square feet, showing that the deal reduces the total area of Frank's property, hence it is not a fair trade area-wise.

Answered by ToddBoyce | 2024-06-24

Frank's original land area is reduced by 9 square feet due to the city's changes. Since he loses area instead of gaining it, the deal is not fair. Frank should not accept the city's compensation as it diminishes his land.
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Answered by ollieboyne | 2024-12-26