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 : 7. If the area of H is 247 cm
2, what is the area of the rectangle DEFG?
L |
K |
J |
H |
1x5 |
4x5 |
|
|
|
5x4 |
7x4 |
|
5 u |
20 u |
28 u |
13 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 + 28 u
= 33 u
Area of H
= Half of the area of the rectangle - Area K
= 33 u - 20 u
= 13 u
13 u = 247
1 u = 247 ÷ 13 = 19
Area of the rectangle
= 33 u x 2
= 66 u
= 66 x 19
= 1254 cm
2 Answer(s): 1254 cm
2