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 7 : 9. If the area of K is 286 cm
2, what is the area of the rectangle FGHJ?
N |
M |
L |
K |
1x7 |
2x7 |
|
|
|
7x2 |
9x2 |
|
7 u |
14 u |
18 u |
11 u |
Area M is the repeated identity.
LCM of 2 and 7 = 14
Half of the area of the rectangle
= Area N + Area L
= 7 u + 18 u
= 25 u
Area of K
= Half of the area of the rectangle - Area M
= 25 u - 14 u
= 11 u
11 u = 286
1 u = 286 ÷ 11 = 26
Area of the rectangle
= 25 u x 2
= 50 u
= 50 x 26
= 1300 cm
2 Answer(s): 1300 cm
2