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 8 : 9. If the area of H is 51 cm
2, what is the area of the rectangle DEFG?
L |
K |
J |
H |
1x2 |
4x2 |
|
|
|
8x1 |
9x1 |
|
2 u |
8 u |
9 u |
3 u |
Area K is the repeated identity.
LCM of 4 and 8 = 8
Half of the area of the rectangle
= Area L + Area J
= 2 u + 9 u
= 11 u
Area of H
= Half of the area of the rectangle - Area K
= 11 u - 8 u
= 3 u
3 u = 51
1 u = 51 ÷ 3 = 17
Area of the rectangle
= 11 u x 2
= 22 u
= 22 x 17
= 374 cm
2 Answer(s): 374 cm
2