The figure, not drawn to scale, shows a rectangle, FGHJ, which is divided in 4 parts, K, L, M, and N. The ratio of the area of N to the area of M is 1 : 2. The ratio of the area of M to the area of L is 9 : 10. If the area of K is 143 cm
2, what is the area of the rectangle FGHJ?
N |
M |
L |
K |
1x9 |
2x9 |
|
|
|
9x2 |
10x2 |
|
9 u |
18 u |
20 u |
11 u |
Area M is the repeated identity.
LCM of 2 and 9 = 18
Half of the area of the rectangle
= Area N + Area L
= 9 u + 20 u
= 29 u
Area of K
= Half of the area of the rectangle - Area M
= 29 u - 18 u
= 11 u
11 u = 143
1 u = 143 ÷ 11 = 13
Area of the rectangle
= 29 u x 2
= 58 u
= 58 x 13
= 754 cm
2 Answer(s): 754 cm
2