The rectangle is divided into four parts R, S, T and U. The ratio of Part R to Part S is 7 : 3 and the ratio of Part S to Part T is 4 : 1.
- Find the ratio of Part R to Part S to Part T.
- Given that Part U is 74 m2 , find the area of the rectangle.
(a)
| R |
S |
T |
U |
| 7x4 |
3x4 |
|
|
| |
4x3 |
1x3 |
|
| 28 u |
12 u |
3 u |
74 m2 |
Part S is the repeated identity.
LCM of 3 and 4 = 12
Part R : Part S : Part T = 28 : 12 : 3
(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
28 u + 12 u = 3 u + 74
28 u + 12 u - 3 u = 74
37 u = 74
1 u = 74 ÷ 37 = 2
Area of the rectangle
= 2 x (3 u + 74)
= 2 x (3 x 2 + 74)
= 2 x (6 + 74)
= 2 x 80
= 160 m
2 Answer(s): (a) 28 : 12 : 3; (b) 160 m
2 
