The area of the rectangle to the area of the triangle in the figure is in the ratio 6 : 7. After the shaded rectangle of width 8 cm is removed from the figure, the ratio of the remaining area of the rectangle to the remaining area of the triangle is 7 : 9. Given that the area of the triangle is 48 cm² more than the area of the rectangle, find the length of the shaded rectangle that is being removed.

	Rectangle	Triangle	Difference
Total	6x2 = 12 u	7x2 = 14 u	1x2 = 2 u
Removed	- 5 u	- 5 u
Left	7 u	9 u	2 u

The difference in the areas between the rectangle and the triangle remains unchanged. Make the difference the same. LCM of 1 and 2 is 2.

Difference in areas between the triangle and the rectangle
= 14 u - 12 u
= 2 u

2 u = 48 

1 u = 48 ÷ 2 = 24

Area of the rectangle that is removed
= 5 u
= 5 x 24
= 120 cm²

Length of the shaded rectangle that is removed
= 120 ÷ 8
= 15 cm

Answer(s): 15 cm