The rectangle is divided into four parts S, T, U and V. The ratio of Part S to Part T is 9 : 2 and the ratio of Part T to Part U is 3 : 2.
- Find the ratio of Part S to Part T to Part U.
- Given that Part V is 58 cm2 , find the area of the rectangle.
(a)
| S |
T |
U |
V |
| 9x3 |
2x3 |
|
|
| |
3x2 |
2x2 |
|
| 27 u |
6 u |
4 u |
58 cm2 |
Part T is the repeated identity.
LCM of 2 and 3 = 6
Part S : Part T : Part U = 27 : 6 : 4
(b)
Part S + Part T = Half of the rectangle
Part U + Part V = Half of the rectangle
Part S + Part T and Part U + Part V are equal.
Part S + Part T = Part U + Part V
27 u + 6 u = 4 u + 58
27 u + 6 u - 4 u = 58
29 u = 58
1 u = 58 ÷ 29 = 2
Area of the rectangle
= 2 x (4 u + 58)
= 2 x (4 x 2 + 58)
= 2 x (8 + 58)
= 2 x 66
= 132 cm
2 Answer(s): (a) 27 : 6 : 4; (b) 132 cm
2 
