The rectangle is divided into four parts P, Q, R and S. The ratio of Part P to Part Q is 8 : 1 and the ratio of Part Q to Part R is 3 : 1.
- Find the ratio of Part P to Part Q to Part R.
- Given that Part S is 78 cm2 , find the area of the rectangle.
(a)
| P |
Q |
R |
S |
| 8x3 |
1x3 |
|
|
| |
3x1 |
1x1 |
|
| 24 u |
3 u |
1 u |
78 cm2 |
Part Q is the repeated identity.
LCM of 1 and 3 = 3
Part P : Part Q : Part R = 24 : 3 : 1
(b)
Part P + Part Q = Half of the rectangle
Part R + Part S = Half of the rectangle
Part P + Part Q and Part R + Part S are equal.
Part P + Part Q = Part R + Part S
24 u + 3 u = 1 u + 78
24 u + 3 u - 1 u = 78
26 u = 78
1 u = 78 ÷ 26 = 3
Area of the rectangle
= 2 x (1 u + 78)
= 2 x (1 x 3 + 78)
= 2 x (3 + 78)
= 2 x 81
= 162 cm
2 Answer(s): (a) 24 : 3 : 1; (b) 162 cm
2 
