The figure, not drawn to scale, shows a rectangle, BCDE, which is divided in 4 parts, F, G, H, and J. The ratio of the area of J to the area of H is 1 : 2. The ratio of the area of H to the area of G is 9 : 10. If the area of F is 275 cm
2, what is the area of the rectangle BCDE?
J |
H |
G |
F |
1x9 |
2x9 |
|
|
|
9x2 |
10x2 |
|
9 u |
18 u |
20 u |
11 u |
Area H is the repeated identity.
LCM of 2 and 9 = 18
Half of the area of the rectangle
= Area J + Area G
= 9 u + 20 u
= 29 u
Area of F
= Half of the area of the rectangle - Area H
= 29 u - 18 u
= 11 u
11 u = 275
1 u = 275 ÷ 11 = 25
Area of the rectangle
= 29 u x 2
= 58 u
= 58 x 25
= 1450 cm
2 Answer(s): 1450 cm
2