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 6 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 54 cm
2 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 = 54
1 u = 54 ÷ 3 = 18
Area of the rectangle that is removed
= 7 u
= 7 x 18
= 126 cm
2 Length of the shaded rectangle that is removed
= 126 ÷ 6
= 21 cm
Answer(s): 21 cm