The area of the rectangle to the area of the triangle in the figure is in the ratio 4 : 5. After the shaded rectangle of width 10 cm is removed from the figure, the ratio of the remaining area of the rectangle to the remaining area of the triangle is 5 : 8. Given that the area of the triangle is 60 cm² more than the area of the rectangle, find the length of the shaded rectangle that is being removed.

	Rectangle	Triangle	Difference
Total	4x3 = 12 u	5x3 = 15 u	1x3 = 3 u
Removed	- 7 u	- 7 u
Left	5 u	8 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
= 15 u - 12 u
= 3 u

3 u = 60 

1 u = 60 ÷ 3 = 20

Area of the rectangle that is removed
= 7 u
= 7 x 20
= 140 cm²

Length of the shaded rectangle that is removed
= 140 ÷ 10
= 14 cm

Answer(s): 14 cm