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 : 4. The ratio of the area of H to the area of G is 8 : 9. If the area of F is 69 cm
2, what is the area of the rectangle BCDE?
J |
H |
G |
F |
1x2 |
4x2 |
|
|
|
8x1 |
9x1 |
|
2 u |
8 u |
9 u |
3 u |
Area H is the repeated identity.
LCM of 4 and 8 = 8
Half of the area of the rectangle
= Area J + Area G
= 2 u + 9 u
= 11 u
Area of F
= Half of the area of the rectangle - Area H
= 11 u - 8 u
= 3 u
3 u = 69
1 u = 69 ÷ 3 = 23
Area of the rectangle
= 11 u x 2
= 22 u
= 22 x 23
= 506 cm
2 Answer(s): 506 cm
2