The rectangle is divided into four parts U, V, W and X. The ratio of Part U to Part V is 10 : 3 and the ratio of Part V to Part W is 3 : 2.
- Find the ratio of Part U to Part V to Part W.
- Given that Part X is 66 m2 , find the area of the rectangle.
(a)
| U |
V |
W |
X |
| 10x1 |
3x1 |
|
|
| |
3x1 |
2x1 |
|
| 10 u |
3 u |
2 u |
66 m2 |
Part V is the repeated identity.
LCM of 3 and 3 = 3
Part U : Part V : Part W = 10 : 3 : 2
(b)
Part U + Part V = Half of the rectangle
Part W + Part X = Half of the rectangle
Part U + Part V and Part W + Part X are equal.
Part U + Part V = Part W + Part X
10 u + 3 u = 2 u + 66
10 u + 3 u - 2 u = 66
11 u = 66
1 u = 66 ÷ 11 = 6
Area of the rectangle
= 2 x (2 u + 66)
= 2 x (2 x 6 + 66)
= 2 x (12 + 66)
= 2 x 78
= 156 m
2 Answer(s): (a) 10 : 3 : 2; (b) 156 m
2 
