The figure, not drawn to scale, shows a rectangle, HJKL, which is divided in 4 parts, M, N, P, and Q. The ratio of the area of Q to the area of P is 1 : 2. The ratio of the area of P to the area of N is 5 : 7. If the area of M is 144 cm
2, what is the area of the rectangle HJKL?
| Q |
P |
N |
M |
| 1x5 |
2x5 |
|
|
| |
5x2 |
7x2 |
|
| 5 u |
10 u |
14 u |
9 u |
Area P is the repeated identity.
LCM of 2 and 5 = 10
Half of the area of the rectangle
= Area Q + Area N
= 5 u + 14 u
= 19 u
Area of M
= Half of the area of the rectangle - Area P
= 19 u - 10 u
= 9 u
9 u = 144
1 u = 144 ÷ 9 = 16
Area of the rectangle
= 19 u x 2
= 38 u
= 38 x 16
= 608 cm
2 Answer(s): 608 cm
2 
