The figure, not drawn to scale, shows a rectangle, DEFG, which is divided in 4 parts, H, J, K, and L. The ratio of the area of L to the area of K is 1 : 4. The ratio of the area of K to the area of J is 5 : 6. If the area of H is 144 cm
2, what is the area of the rectangle DEFG?
L |
K |
J |
H |
1x5 |
4x5 |
|
|
|
5x4 |
6x4 |
|
5 u |
20 u |
24 u |
9 u |
Area K is the repeated identity.
LCM of 4 and 5 = 20
Half of the area of the rectangle
= Area L + Area J
= 5 u + 24 u
= 29 u
Area of H
= Half of the area of the rectangle - Area K
= 29 u - 20 u
= 9 u
9 u = 144
1 u = 144 ÷ 9 = 16
Area of the rectangle
= 29 u x 2
= 58 u
= 58 x 16
= 928 cm
2 Answer(s): 928 cm
2