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 2 : 7. The ratio of the area of L to the area of K is 8 : 9. If the area of J is 667 cm
2, what is the area of the rectangle EFGH?
M |
L |
K |
J |
2x8 |
7x8 |
|
|
|
8x7 |
9x7 |
|
16 u |
56 u |
63 u |
23 u |
Area L is the repeated identity.
LCM of 7 and 8 = 56
Half of the area of the rectangle
= Area M + Area K
= 16 u + 63 u
= 79 u
Area of J
= Half of the area of the rectangle - Area L
= 79 u - 56 u
= 23 u
23 u = 667
1 u = 667 ÷ 23 = 29
Area of the rectangle
= 79 u x 2
= 158 u
= 158 x 29
= 4582 cm
2 Answer(s): 4582 cm
2