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 : 8. If the area of K is 261 cm
2, what is the area of the rectangle FGHJ?
N |
M |
L |
K |
1x7 |
2x7 |
|
|
|
7x2 |
8x2 |
|
7 u |
14 u |
16 u |
9 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 + 16 u
= 23 u
Area of K
= Half of the area of the rectangle - Area M
= 23 u - 14 u
= 9 u
9 u = 261
1 u = 261 ÷ 9 = 29
Area of the rectangle
= 23 u x 2
= 46 u
= 46 x 29
= 1334 cm
2 Answer(s): 1334 cm
2