Determine the dimensions of a rectangle having a perimeter of cm and an area of .
Let the length of the rectangle be denoted by and the width of the rectangle be denoted by . If the perimeter of the rectangle is , then
which simplifies to
If the area of the rectangle is , then
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.
Now substitute each value into the first order equation to find .
The dimensions of the rectangle are therefore and .