The figure, not drawn to scale, shows a rectangle, ABCD, which is divided in 4 parts, E, F, G, and H. The ratio of the area of H to the area of G is 1 : 2. The ratio of the area of G to the area of F is 5 : 7. If the area of E is 135 cm
2, what is the area of the rectangle ABCD?
H |
G |
F |
E |
1x5 |
2x5 |
|
|
|
5x2 |
7x2 |
|
5 u |
10 u |
14 u |
9 u |
Area G is the repeated identity.
LCM of 2 and 5 = 10
Half of the area of the rectangle
= Area H + Area F
= 5 u + 14 u
= 19 u
Area of E
= Half of the area of the rectangle - Area G
= 19 u - 10 u
= 9 u
9 u = 135
1 u = 135 ÷ 9 = 15
Area of the rectangle
= 19 u x 2
= 38 u
= 38 x 15
= 570 cm
2 Answer(s): 570 cm
2