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 2 : 7. The ratio of the area of H to the area of G is 4 : 5. If the area of F is 390 cm
2, what is the area of the rectangle BCDE?
J |
H |
G |
F |
2x4 |
7x4 |
|
|
|
4x7 |
5x7 |
|
8 u |
28 u |
35 u |
15 u |
Area H is the repeated identity.
LCM of 7 and 4 = 28
Half of the area of the rectangle
= Area J + Area G
= 8 u + 35 u
= 43 u
Area of F
= Half of the area of the rectangle - Area H
= 43 u - 28 u
= 15 u
15 u = 390
1 u = 390 ÷ 15 = 26
Area of the rectangle
= 43 u x 2
= 86 u
= 86 x 26
= 2236 cm
2 Answer(s): 2236 cm
2