If the length of a rectangle increases by 2 cm, its
area will increase by 12 cm^{2}. If the width increases by 3 cm, its
area will increase by 21cm^{2}. What is the original area of the
rectangle? cm^{2}

By increasing the length by 2 cm, we are basically
adding a rectangle that is 2 cm by the width of the original rectangle. Since
the area of the added rectangle is 12, the width of the original rectangle is
therefore 12 ÷ 2 = 6 cm. By increasing the
width by 3 cm, we are basically adding a rectangle that is 3 cm by the length
of the original rectangle. Since the area of this added rectangle is 21, the
length is 21 ÷ 3 = 7cm. Thus the original
rectangle has an area of 7 × 6 = 42 cm^{2}.