The figure, not drawn to scale, shows a rectangle, EFGH, which is divided in 4 parts, J, K, L, and M. The ratio of the area of M to the area of L is 1 : 3. The ratio of the area of L to the area of K is 6 : 7. If the area of J is 57 cm
2, what is the area of the rectangle EFGH?
| M |
L |
K |
J |
| 1x2 |
3x2 |
|
|
| |
6x1 |
7x1 |
|
| 2 u |
6 u |
7 u |
3 u |
Area L is the repeated identity.
LCM of 3 and 6 = 6
Half of the area of the rectangle
= Area M + Area K
= 2 u + 7 u
= 9 u
Area of J
= Half of the area of the rectangle - Area L
= 9 u - 6 u
= 3 u
3 u = 57
1 u = 57 ÷ 3 = 19
Area of the rectangle
= 9 u x 2
= 18 u
= 18 x 19
= 342 cm
2 Answer(s): 342 cm
2 
