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 : 3. The ratio of the area of M to the area of L is 8 : 9. If the area of K is 176 cm
2, what is the area of the rectangle FGHJ?
N |
M |
L |
K |
1x8 |
3x8 |
|
|
|
8x3 |
9x3 |
|
8 u |
24 u |
27 u |
11 u |
Area M is the repeated identity.
LCM of 3 and 8 = 24
Half of the area of the rectangle
= Area N + Area L
= 8 u + 27 u
= 35 u
Area of K
= Half of the area of the rectangle - Area M
= 35 u - 24 u
= 11 u
11 u = 176
1 u = 176 ÷ 11 = 16
Area of the rectangle
= 35 u x 2
= 70 u
= 70 x 16
= 1120 cm
2 Answer(s): 1120 cm
2