The figure, not drawn to scale, on the right shows 2 rectangles overlapping each other. The ratio of the shaded area to the area of Rectangle P is 5 : 8. The ratio of the shaded area to the area of Rectangle Q is 2 : 5. Find the ratio of the unshaded area to the total area of the figure.
Rectangle P |
Shaded Area |
Rectangle Q |
8 x 2 |
5 x 2 |
|
|
2 x 5 |
5 x 5 |
16 u |
10 u |
25 u |
The shaded area is the same for both rectangles.
LCM of 2 and 5 = 10
Total area of the figure
= 16 u + 25 u - 10 u
= 31 u
Unshaded area
= 31 u - 10 u
= 21 u
Unshaded area : Total area of the figure
21 : 31
Answer(s): 21 : 31