The area of the rectangle to the area of the triangle in the figure is in the ratio 6 : 7. 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 7 : 9. Given that the area of the triangle is 32 cm
2 more than the area of the rectangle, find the width of the shaded rectangle that is being removed.
|
Rectangle |
Triangle |
Difference |
Total |
6x2 = 12 u |
7x2 = 14 u |
1x2 = 2 u |
Removed |
- 5 u |
- 5 u |
|
Left |
7 u |
9 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
= 14 u - 12 u
= 2 u
2 u = 32
1 u = 32 ÷ 2 = 16
Area of the rectangle that is removed
= 5 u
= 5 x 16
= 80 cm
2 Width of the shaded rectangle that is removed
= 80 ÷ 10
= 8 cm
Answer(s): 8 cm