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 5 : 6. If the area of G is 255 cm
2, what is the area of the rectangle CDEF?
K |
J |
H |
G |
2x5 |
7x5 |
|
|
|
5x7 |
6x7 |
|
10 u |
35 u |
42 u |
17 u |
Area J is the repeated identity.
LCM of 7 and 5 = 35
Half of the area of the rectangle
= Area K + Area H
= 10 u + 42 u
= 52 u
Area of G
= Half of the area of the rectangle - Area J
= 52 u - 35 u
= 17 u
17 u = 255
1 u = 255 ÷ 17 = 15
Area of the rectangle
= 52 u x 2
= 104 u
= 104 x 15
= 1560 cm
2 Answer(s): 1560 cm
2