The figure, not drawn to scale, shows a rectangle, CDEF, which is divided in 4 parts, G, H, J, and K. The ratio of the area of K to the area of J is 2 : 7. The ratio of the area of J to the area of H is 6 : 7. If the area of G is 247 cm
2, what is the area of the rectangle CDEF?
K |
J |
H |
G |
2x6 |
7x6 |
|
|
|
6x7 |
7x7 |
|
12 u |
42 u |
49 u |
19 u |
Area J is the repeated identity.
LCM of 7 and 6 = 42
Half of the area of the rectangle
= Area K + Area H
= 12 u + 49 u
= 61 u
Area of G
= Half of the area of the rectangle - Area J
= 61 u - 42 u
= 19 u
19 u = 247
1 u = 247 ÷ 19 = 13
Area of the rectangle
= 61 u x 2
= 122 u
= 122 x 13
= 1586 cm
2 Answer(s): 1586 cm
2