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 : 7. The ratio of the area of K to the area of J is 5 : 7. If the area of H is 312 cm
2, what is the area of the rectangle DEFG?
L |
K |
J |
H |
2x5 |
7x5 |
|
|
|
5x7 |
7x7 |
|
10 u |
35 u |
49 u |
24 u |
Area K is the repeated identity.
LCM of 7 and 5 = 35
Half of the area of the rectangle
= Area L + Area J
= 10 u + 49 u
= 59 u
Area of H
= Half of the area of the rectangle - Area K
= 59 u - 35 u
= 24 u
24 u = 312
1 u = 312 ÷ 24 = 13
Area of the rectangle
= 59 u x 2
= 118 u
= 118 x 13
= 1534 cm
2 Answer(s): 1534 cm
2