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 2 : 5. The ratio of the area of K to the area of J is 7 : 9. If the area of H is 552 cm
2, what is the area of the rectangle DEFG?
L |
K |
J |
H |
2x7 |
5x7 |
|
|
|
7x5 |
9x5 |
|
14 u |
35 u |
45 u |
24 u |
Area K is the repeated identity.
LCM of 5 and 7 = 35
Half of the area of the rectangle
= Area L + Area J
= 14 u + 45 u
= 59 u
Area of H
= Half of the area of the rectangle - Area K
= 59 u - 35 u
= 24 u
24 u = 552
1 u = 552 ÷ 24 = 23
Area of the rectangle
= 59 u x 2
= 118 u
= 118 x 23
= 2714 cm
2 Answer(s): 2714 cm
2