The area of the rectangle to the area of the triangle in the figure is in the ratio 3 : 4. 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 4 : 9. Given that the area of the triangle is 50 cm
2 more than the area of the rectangle, find the length of the shaded rectangle that is being removed.
|
Rectangle |
Triangle |
Difference |
Total |
3x5 = 15 u |
4x5 = 20 u |
1x5 = 5 u |
Removed |
- 11 u |
- 11 u |
|
Left |
4 u |
9 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
= 20 u - 15 u
= 5 u
5 u = 50
1 u = 50 ÷ 5 = 10
Area of the rectangle that is removed
= 11 u
= 11 x 10
= 110 cm
2 Length of the shaded rectangle that is removed
= 110 ÷ 10
= 11 cm
Answer(s): 11 cm