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 : 5. The ratio of the area of L to the area of K is 8 : 9. If the area of J is 420 cm
2, what is the area of the rectangle EFGH?
M |
L |
K |
J |
2x8 |
5x8 |
|
|
|
8x5 |
9x5 |
|
16 u |
40 u |
45 u |
21 u |
Area L is the repeated identity.
LCM of 5 and 8 = 40
Half of the area of the rectangle
= Area M + Area K
= 16 u + 45 u
= 61 u
Area of J
= Half of the area of the rectangle - Area L
= 61 u - 40 u
= 21 u
21 u = 420
1 u = 420 ÷ 21 = 20
Area of the rectangle
= 61 u x 2
= 122 u
= 122 x 20
= 2440 cm
2 Answer(s): 2440 cm
2