The rectangle is divided into four parts T, U, V and W. The ratio of Part T to Part U is 7 : 2 and the ratio of Part U to Part V is 3 : 2.
- Find the ratio of Part T to Part U to Part V.
- Given that Part W is 46 cm2 , find the area of the rectangle.
(a)
| T |
U |
V |
W |
| 7x3 |
2x3 |
|
|
| |
3x2 |
2x2 |
|
| 21 u |
6 u |
4 u |
46 cm2 |
Part U is the repeated identity.
LCM of 2 and 3 = 6
Part T : Part U : Part V = 21 : 6 : 4
(b)
Part T + Part U = Half of the rectangle
Part V + Part W = Half of the rectangle
Part T + Part U and Part V + Part W are equal.
Part T + Part U = Part V + Part W
21 u + 6 u = 4 u + 46
21 u + 6 u - 4 u = 46
23 u = 46
1 u = 46 ÷ 23 = 2
Area of the rectangle
= 2 x (4 u + 46)
= 2 x (4 x 2 + 46)
= 2 x (8 + 46)
= 2 x 54
= 108 cm
2 Answer(s): (a) 21 : 6 : 4; (b) 108 cm
2 
