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 7 cm is removed from the figure, the ratio of the remaining area of the rectangle to the remaining area of the triangle is 5 : 7. Given that the area of the triangle is 56 cm
2 more than the area of the rectangle, find the length of the shaded rectangle that is being removed.
|
Rectangle |
Triangle |
Difference |
Total |
4x2 = 8 u |
5x2 = 10 u |
1x2 = 2 u |
Removed |
- 3 u |
- 3 u |
|
Left |
5 u |
7 u |
2 u |
The difference in the areas between the rectangle and the triangle remains unchanged. Make the difference the same. LCM of 1 and 2 is 2.
Difference in areas between the triangle and the rectangle
= 10 u - 8 u
= 2 u
2 u = 56
1 u = 56 ÷ 2 = 28
Area of the rectangle that is removed
= 3 u
= 3 x 28
= 84 cm
2 Length of the shaded rectangle that is removed
= 84 ÷ 7
= 12 cm
Answer(s): 12 cm