The rectangle is divided into four parts R, S, T and U. The ratio of Part R to Part S is 8 : 3 and the ratio of Part S to Part T is 3 : 2.
- Find the ratio of Part R to Part S to Part T.
- Given that Part U is 54 m2 , find the area of the rectangle.
(a)
| R |
S |
T |
U |
| 8x1 |
3x1 |
|
|
| |
3x1 |
2x1 |
|
| 8 u |
3 u |
2 u |
54 m2 |
Part S is the repeated identity.
LCM of 3 and 3 = 3
Part R : Part S : Part T = 8 : 3 : 2
(b)
Part R + Part S = Half of the rectangle
Part T + Part U = Half of the rectangle
Part R + Part S and Part T + Part U are equal.
Part R + Part S = Part T + Part U
8 u + 3 u = 2 u + 54
8 u + 3 u - 2 u = 54
9 u = 54
1 u = 54 ÷ 9 = 6
Area of the rectangle
= 2 x (2 u + 54)
= 2 x (2 x 6 + 54)
= 2 x (12 + 54)
= 2 x 66
= 132 m
2 Answer(s): (a) 8 : 3 : 2; (b) 132 m
2 
