The length of a rectangle is cm, its width is cm, and its area is . If its length decreased by cm and its width increased by cm, it will become a square. Find the area of the square.
If the area of the rectangle is cm, then
The rectangle would become a square if its length were decreased by cm and its width increased by cm, then the two new dimensions would be the same. Hence,
This pair of equations can be solved by substitution. Rearranging the first order equation gives
Substituting into the second order equation gives
This equation can be solved by factorisation.
As represents the width of a rectangle, it must have a positive value. Therefore, cm.
The side length of the square is given by , and is therefore equal to cm.