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 length 11 cm is removed from the figure, the ratio of the remaining area of the rectangle to the remaining area of the triangle is 4 : 9. Given that the area of the triangle is 30 cm² more than the area of the rectangle, find the width of the shaded rectangle that is being removed.

	Rectangle	Triangle	Difference
Total	3x5 = 15 u	4x5 = 20 u	1x5 = 5 u
Removed	- 11 u	- 11 u
Left	4 u	9 u	5 u

The difference in the areas between the rectangle and the triangle remains unchanged. Make the difference the same. LCM of 1 and 5 is 5.

Difference in areas between the triangle and the rectangle
= 20 u - 15 u
= 5 u

5 u = 30 

1 u = 30 ÷ 5 = 6

Area of the rectangle that is removed
= 11 u
= 11 x 6
= 66 cm²

Width of the shaded rectangle that is removed
= 66 ÷ 11
= 6 cm

Answer(s): 6 cm