The rectangle is divided into four parts K, L, M and N. The ratio of Part K to Part L is 8 : 1 and the ratio of Part L to Part M is 3 : 2.
- Find the ratio of Part K to Part L to Part M.
- Given that Part N is 50 cm2 , find the area of the rectangle.
(a)
| K |
L |
M |
N |
| 8x3 |
1x3 |
|
|
| |
3x1 |
2x1 |
|
| 24 u |
3 u |
2 u |
50 cm2 |
Part L is the repeated identity.
LCM of 1 and 3 = 3
Part K : Part L : Part M = 24 : 3 : 2
(b)
Part K + Part L = Half of the rectangle
Part M + Part N = Half of the rectangle
Part K + Part L and Part M + Part N are equal.
Part K + Part L = Part M + Part N
24 u + 3 u = 2 u + 50
24 u + 3 u - 2 u = 50
25 u = 50
1 u = 50 ÷ 25 = 2
Area of the rectangle
= 2 x (2 u + 50)
= 2 x (2 x 2 + 50)
= 2 x (4 + 50)
= 2 x 54
= 108 cm
2 Answer(s): (a) 24 : 3 : 2; (b) 108 cm
2 
