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 : 2. The ratio of the area of L to the area of K is 7 : 8. If the area of J is 108 cm
2, what is the area of the rectangle EFGH?
M |
L |
K |
J |
1x7 |
2x7 |
|
|
|
7x2 |
8x2 |
|
7 u |
14 u |
16 u |
9 u |
Area L is the repeated identity.
LCM of 2 and 7 = 14
Half of the area of the rectangle
= Area M + Area K
= 7 u + 16 u
= 23 u
Area of J
= Half of the area of the rectangle - Area L
= 23 u - 14 u
= 9 u
9 u = 108
1 u = 108 ÷ 9 = 12
Area of the rectangle
= 23 u x 2
= 46 u
= 46 x 12
= 552 cm
2 Answer(s): 552 cm
2