Answer to Question #3146 in Geometry for Rebecca

Question

A building has a rectangular room and a square room with equal floor space. The rectangular room is 3 meters longer and 2 meters narrower than the square room. Find the floor space of each. Please explain the steps in finding the answer as well.

Answer 1

Let's denote the side of the square room as x. Then the one side of rectangular room is x +3, the other side is x - 2.
Sinse both rooms have an equal area,
x*x = (x+3)(x-2)
x² = x² + x - 6
x = 6.
Thus the floor space of each room is 6² = 36 m^2.