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 2 : 7. The ratio of the area of G to the area of F is 4 : 5. If the area of E is 225 cm
2, what is the area of the rectangle ABCD?
H |
G |
F |
E |
2x4 |
7x4 |
|
|
|
4x7 |
5x7 |
|
8 u |
28 u |
35 u |
15 u |
Area G is the repeated identity.
LCM of 7 and 4 = 28
Half of the area of the rectangle
= Area H + Area F
= 8 u + 35 u
= 43 u
Area of E
= Half of the area of the rectangle - Area G
= 43 u - 28 u
= 15 u
15 u = 225
1 u = 225 ÷ 15 = 15
Area of the rectangle
= 43 u x 2
= 86 u
= 86 x 15
= 1290 cm
2 Answer(s): 1290 cm
2