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 : 7. The ratio of the area of M to the area of L is 4 : 5. If the area of K is 330 cm
2, what is the area of the rectangle FGHJ?
N |
M |
L |
K |
2x4 |
7x4 |
|
|
|
4x7 |
5x7 |
|
8 u |
28 u |
35 u |
15 u |
Area M is the repeated identity.
LCM of 7 and 4 = 28
Half of the area of the rectangle
= Area N + Area L
= 8 u + 35 u
= 43 u
Area of K
= Half of the area of the rectangle - Area M
= 43 u - 28 u
= 15 u
15 u = 330
1 u = 330 ÷ 15 = 22
Area of the rectangle
= 43 u x 2
= 86 u
= 86 x 22
= 1892 cm
2 Answer(s): 1892 cm
2