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 : 9. If the area of K is 456 cm
2, what is the area of the rectangle FGHJ?
N |
M |
L |
K |
2x7 |
5x7 |
|
|
|
7x5 |
9x5 |
|
14 u |
35 u |
45 u |
24 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 + 45 u
= 59 u
Area of K
= Half of the area of the rectangle - Area M
= 59 u - 35 u
= 24 u
24 u = 456
1 u = 456 ÷ 24 = 19
Area of the rectangle
= 59 u x 2
= 118 u
= 118 x 19
= 2242 cm
2 Answer(s): 2242 cm
2