The rectangle is divided into four parts K, L, M and N. The ratio of Part K to Part L is 10 : 3 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 66 cm2 , find the area of the rectangle.
(a)
K |
L |
M |
N |
10x1 |
3x1 |
|
|
|
3x1 |
2x1 |
|
10 u |
3 u |
2 u |
66 cm2 |
Part L is the repeated identity.
LCM of 3 and 3 = 3
Part K : Part L : Part M = 10 : 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
10 u + 3 u = 2 u + 66
10 u + 3 u - 2 u = 66
11 u = 66
1 u = 66 ÷ 11 = 6
Area of the rectangle
= 2 x (2 u + 66)
= 2 x (2 x 6 + 66)
= 2 x (12 + 66)
= 2 x 78
= 156 cm
2 Answer(s): (a) 10 : 3 : 2; (b) 156 cm
2