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 9 cm is removed from the figure, the ratio of the remaining area of the rectangle to the remaining area of the triangle is 5 : 9. Given that the area of the triangle is 72 cm
2 more than the area of the rectangle, find the length of the shaded rectangle that is being removed.
|
Rectangle |
Triangle |
Difference |
Total |
4x4 = 16 u |
5x4 = 20 u |
1x4 = 4 u |
Removed |
- 11 u |
- 11 u |
|
Left |
5 u |
9 u |
4 u |
The difference in the areas between the rectangle and the triangle remains unchanged. Make the difference the same. LCM of 1 and 4 is 4.
Difference in areas between the triangle and the rectangle
= 20 u - 16 u
= 4 u
4 u = 72
1 u = 72 ÷ 4 = 18
Area of the rectangle that is removed
= 11 u
= 11 x 18
= 198 cm
2 Length of the shaded rectangle that is removed
= 198 ÷ 9
= 22 cm
Answer(s): 22 cm