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 : 4. The ratio of the area of M to the area of L is 5 : 7. If the area of K is 208 cm
2, what is the area of the rectangle FGHJ?
N |
M |
L |
K |
1x5 |
4x5 |
|
|
|
5x4 |
7x4 |
|
5 u |
20 u |
28 u |
13 u |
Area M is the repeated identity.
LCM of 4 and 5 = 20
Half of the area of the rectangle
= Area N + Area L
= 5 u + 28 u
= 33 u
Area of K
= Half of the area of the rectangle - Area M
= 33 u - 20 u
= 13 u
13 u = 208
1 u = 208 ÷ 13 = 16
Area of the rectangle
= 33 u x 2
= 66 u
= 66 x 16
= 1056 cm
2 Answer(s): 1056 cm
2