Answer:

The first floor is 25 feet square, and the second floor is 15 feet square.

Here's how you solve it.

Let x represent the length of the side of the second floor.

Then the area of the second floor is x² square feet.

The length of the side of the first floor is (x+10) feet.

So the area of the first floor is (x+10)² square feet.

The total area, 850 square feet, can be represented by the following equation:

x² + (x+10)² = 850
x² + x² + 20x + 100 = 850
2x² + 20x - 750 = 0
x² + 10x - 375 = 0
(x+25)(x-15) = 0

So x is either 15 or it is negative twenty five.  Negative answers don't make sense, so x=15.  The answer follows.