The rectangle is divided into four parts A, B, C and D. The ratio of Part A to Part B is 9 : 4 and the ratio of Part B to Part C is 4 : 1.
- Find the ratio of Part A to Part B to Part C.
- Given that Part D is 48 m2 , find the area of the rectangle.
(a)
| A |
B |
C |
D |
| 9x1 |
4x1 |
|
|
| |
4x1 |
1x1 |
|
| 9 u |
4 u |
1 u |
48 m2 |
Part B is the repeated identity.
LCM of 4 and 4 = 4
Part A : Part B : Part C = 9 : 4 : 1
(b)
Part A + Part B = Half of the rectangle
Part C + Part D = Half of the rectangle
Part A + Part B and Part C + Part D are equal.
Part A + Part B = Part C + Part D
9 u + 4 u = 1 u + 48
9 u + 4 u - 1 u = 48
12 u = 48
1 u = 48 ÷ 12 = 4
Area of the rectangle
= 2 x (1 u + 48)
= 2 x (1 x 4 + 48)
= 2 x (4 + 48)
= 2 x 52
= 104 m
2 Answer(s): (a) 9 : 4 : 1; (b) 104 m
2 
