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 : 9. If the area of J is 220 cm
2, what is the area of the rectangle EFGH?
M |
L |
K |
J |
1x7 |
2x7 |
|
|
|
7x2 |
9x2 |
|
7 u |
14 u |
18 u |
11 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 + 18 u
= 25 u
Area of J
= Half of the area of the rectangle - Area L
= 25 u - 14 u
= 11 u
11 u = 220
1 u = 220 ÷ 11 = 20
Area of the rectangle
= 25 u x 2
= 50 u
= 50 x 20
= 1000 cm
2 Answer(s): 1000 cm
2