Question

Frank owns an entire city block, which happens to be a perfectly square piece of land. One corner of the block is in the intersection of slauson ave. and Carmelita . Because of 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?
Please help me

Answer 1

So originally, let's say the width of Frank's land was $x$ feet.

The area of his land was therefore $x \times x$, 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:

$(x+3)(x-3)\\=x^2+3x-3x-9\\=x^2-9$

So the new land is now 9 square feet smaller, so it is not a fair deal for Frank.

Hope this helps :)