The rectangle is divided into four parts U, V, W and X. The ratio of Part U to Part V is 7 : 2 and the ratio of Part V to Part W is 4 : 1.
- Find the ratio of Part U to Part V to Part W.
- Given that Part X is 85 m2 , find the area of the rectangle.
(a)
| U |
V |
W |
X |
| 7x2 |
2x2 |
|
|
| |
4x1 |
1x1 |
|
| 14 u |
4 u |
1 u |
85 m2 |
Part V is the repeated identity.
LCM of 2 and 4 = 4
Part U : Part V : Part W = 14 : 4 : 1
(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
14 u + 4 u = 1 u + 85
14 u + 4 u - 1 u = 85
17 u = 85
1 u = 85 ÷ 17 = 5
Area of the rectangle
= 2 x (1 u + 85)
= 2 x (1 x 5 + 85)
= 2 x (5 + 85)
= 2 x 90
= 180 m
2 Answer(s): (a) 14 : 4 : 1; (b) 180 m
2 
