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 length 10 cm is removed from the figure, the ratio of the remaining area of the rectangle to the remaining area of the triangle is 3 : 7. Given that the area of the triangle is 40 cm
2 more than the area of the rectangle, find the width of the shaded rectangle that is being removed.
|
Rectangle |
Triangle |
Difference |
Total |
2x4 = 8 u |
3x4 = 12 u |
1x4 = 4 u |
Removed |
- 5 u |
- 5 u |
|
Left |
3 u |
7 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
= 12 u - 8 u
= 4 u
4 u = 40
1 u = 40 ÷ 4 = 10
Area of the rectangle that is removed
= 5 u
= 5 x 10
= 50 cm
2 Width of the shaded rectangle that is removed
= 50 ÷ 10
= 5 cm
Answer(s): 5 cm