The figure, not drawn to scale, shows a rectangle, EFGH, which is divided in 4 parts, J, K, L, and M. The ratio of the area of M to the area of L is 1 : 2. The ratio of the area of L to the area of K is 8 : 9. If the area of J is 130 cm
2, what is the area of the rectangle EFGH?
M |
L |
K |
J |
1x4 |
2x4 |
|
|
|
8x1 |
9x1 |
|
4 u |
8 u |
9 u |
5 u |
Area L is the repeated identity.
LCM of 2 and 8 = 8
Half of the area of the rectangle
= Area M + Area K
= 4 u + 9 u
= 13 u
Area of J
= Half of the area of the rectangle - Area L
= 13 u - 8 u
= 5 u
5 u = 130
1 u = 130 ÷ 5 = 26
Area of the rectangle
= 13 u x 2
= 26 u
= 26 x 26
= 676 cm
2 Answer(s): 676 cm
2