The figure, not drawn to scale, shows a rectangle, GHJK, which is divided in 4 parts, L, M, N, and P. The ratio of the area of P to the area of N is 1 : 3. The ratio of the area of N to the area of M is 5 : 6. If the area of L is 128 cm
2, what is the area of the rectangle GHJK?
P |
N |
M |
L |
1x5 |
3x5 |
|
|
|
5x3 |
6x3 |
|
5 u |
15 u |
18 u |
8 u |
Area N is the repeated identity.
LCM of 3 and 5 = 15
Half of the area of the rectangle
= Area P + Area M
= 5 u + 18 u
= 23 u
Area of L
= Half of the area of the rectangle - Area N
= 23 u - 15 u
= 8 u
8 u = 128
1 u = 128 ÷ 8 = 16
Area of the rectangle
= 23 u x 2
= 46 u
= 46 x 16
= 736 cm
2 Answer(s): 736 cm
2