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 5 : 6. If the area of F is 161 cm
2, what is the area of the rectangle BCDE?
J |
H |
G |
F |
1x5 |
2x5 |
|
|
|
5x2 |
6x2 |
|
5 u |
10 u |
12 u |
7 u |
Area H is the repeated identity.
LCM of 2 and 5 = 10
Half of the area of the rectangle
= Area J + Area G
= 5 u + 12 u
= 17 u
Area of F
= Half of the area of the rectangle - Area H
= 17 u - 10 u
= 7 u
7 u = 161
1 u = 161 ÷ 7 = 23
Area of the rectangle
= 17 u x 2
= 34 u
= 34 x 23
= 782 cm
2 Answer(s): 782 cm
2