An artist has completed one-fourth of a rectangular oil painting. When he paint another 100 square centimetres of the painting, he would complete three-quarters of the painting. If the height of the oil painting is 10 cm, determine the length (in cm) of the oil panting.

Correct Answer: 20 cm
Let the area of the whole painting be x cm2
Then,
$$\eqalign{ & \Rightarrow \frac{1}{4}x + 100 = \frac{3}{4}x \cr & \Rightarrow \frac{1}{2}x = 100 \cr & \Rightarrow x = 200 \cr} $$
∴ Area of painting = 200 cm2
And, Height = 10 cm
Length of painting :
$$\eqalign{ & = \left( {\frac{{200}}{{10}}} \right)cm \cr & = 20\,\,cm \cr} $$