The area of the rectangle to the area of the triangle in the figure is in the ratio 3 : 4. After the shaded rectangle of width 9 cm is removed from the figure, the ratio of the remaining area of the rectangle to the remaining area of the triangle is 4 : 7. Given that the area of the triangle is 81 cm² more than the area of the rectangle, find the length of the shaded rectangle that is being removed.

	Rectangle	Triangle	Difference
Total	3x3 = 9 u	4x3 = 12 u	1x3 = 3 u
Removed	- 5 u	- 5 u
Left	4 u	7 u	3 u

The difference in the areas between the rectangle and the triangle remains unchanged. Make the difference the same. LCM of 1 and 3 is 3.

Difference in areas between the triangle and the rectangle
= 12 u - 9 u
= 3 u

3 u = 81 

1 u = 81 ÷ 3 = 27

Area of the rectangle that is removed
= 5 u
= 5 x 27
= 135 cm²

Length of the shaded rectangle that is removed
= 135 ÷ 9
= 15 cm

Answer(s): 15 cm