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 : 3. The ratio of the area of H to the area of G is 5 : 6. If the area of F is 104 cm
2, what is the area of the rectangle BCDE?
J |
H |
G |
F |
1x5 |
3x5 |
|
|
|
5x3 |
6x3 |
|
5 u |
15 u |
18 u |
8 u |
Area H is the repeated identity.
LCM of 3 and 5 = 15
Half of the area of the rectangle
= Area J + Area G
= 5 u + 18 u
= 23 u
Area of F
= Half of the area of the rectangle - Area H
= 23 u - 15 u
= 8 u
8 u = 104
1 u = 104 ÷ 8 = 13
Area of the rectangle
= 23 u x 2
= 46 u
= 46 x 13
= 598 cm
2 Answer(s): 598 cm
2