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 5 : 7. If the area of F is 576 cm
2, what is the area of the rectangle BCDE?
J |
H |
G |
F |
2x5 |
7x5 |
|
|
|
5x7 |
7x7 |
|
10 u |
35 u |
49 u |
24 u |
Area H is the repeated identity.
LCM of 7 and 5 = 35
Half of the area of the rectangle
= Area J + Area G
= 10 u + 49 u
= 59 u
Area of F
= Half of the area of the rectangle - Area H
= 59 u - 35 u
= 24 u
24 u = 576
1 u = 576 ÷ 24 = 24
Area of the rectangle
= 59 u x 2
= 118 u
= 118 x 24
= 2832 cm
2 Answer(s): 2832 cm
2