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 2 : 5. The ratio of the area of M to the area of L is 7 : 8. If the area of K is 551 cm
2, what is the area of the rectangle FGHJ?
N |
M |
L |
K |
2x7 |
5x7 |
|
|
|
7x5 |
8x5 |
|
14 u |
35 u |
40 u |
19 u |
Area M is the repeated identity.
LCM of 5 and 7 = 35
Half of the area of the rectangle
= Area N + Area L
= 14 u + 40 u
= 54 u
Area of K
= Half of the area of the rectangle - Area M
= 54 u - 35 u
= 19 u
19 u = 551
1 u = 551 ÷ 19 = 29
Area of the rectangle
= 54 u x 2
= 108 u
= 108 x 29
= 3132 cm
2 Answer(s): 3132 cm
2