The area of the rectangle to the area of the triangle in the figure is in the ratio 2 : 3. 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 3 : 8. Given that the area of the triangle is 80 cm
2 more than the area of the rectangle, find the length of the shaded rectangle that is being removed.
|
Rectangle |
Triangle |
Difference |
Total |
2x5 = 10 u |
3x5 = 15 u |
1x5 = 5 u |
Removed |
- 7 u |
- 7 u |
|
Left |
3 u |
8 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
= 15 u - 10 u
= 5 u
5 u = 80
1 u = 80 ÷ 5 = 16
Area of the rectangle that is removed
= 7 u
= 7 x 16
= 112 cm
2 Length of the shaded rectangle that is removed
= 112 ÷ 8
= 14 cm
Answer(s): 14 cm