The rectangle is divided into four parts M, N, P and Q. The ratio of Part M to Part N is 10 : 3 and the ratio of Part N to Part P is 3 : 1.
- Find the ratio of Part M to Part N to Part P.
- Given that Part Q is 72 cm2 , find the area of the rectangle.
(a)
| M |
N |
P |
Q |
| 10x1 |
3x1 |
|
|
| |
3x1 |
1x1 |
|
| 10 u |
3 u |
1 u |
72 cm2 |
Part N is the repeated identity.
LCM of 3 and 3 = 3
Part M : Part N : Part P = 10 : 3 : 1
(b)
Part M + Part N = Half of the rectangle
Part P + Part Q = Half of the rectangle
Part M + Part N and Part P + Part Q are equal.
Part M + Part N = Part P + Part Q
10 u + 3 u = 1 u + 72
10 u + 3 u - 1 u = 72
12 u = 72
1 u = 72 ÷ 12 = 6
Area of the rectangle
= 2 x (1 u + 72)
= 2 x (1 x 6 + 72)
= 2 x (6 + 72)
= 2 x 78
= 156 cm
2 Answer(s): (a) 10 : 3 : 1; (b) 156 cm
2 
