The rectangle is divided into four parts K, L, M and N. The ratio of Part K to Part L is 10 : 1 and the ratio of Part L to Part M is 3 : 1.
- Find the ratio of Part K to Part L to Part M.
- Given that Part N is 32 cm2 , find the area of the rectangle.
(a)
K |
L |
M |
N |
10x3 |
1x3 |
|
|
|
3x1 |
1x1 |
|
30 u |
3 u |
1 u |
32 cm2 |
Part L is the repeated identity.
LCM of 1 and 3 = 3
Part K : Part L : Part M = 30 : 3 : 1
(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
30 u + 3 u = 1 u + 32
30 u + 3 u - 1 u = 32
32 u = 32
1 u = 32 ÷ 32 = 1
Area of the rectangle
= 2 x (1 u + 32)
= 2 x (1 x 1 + 32)
= 2 x (1 + 32)
= 2 x 33
= 66 cm
2 Answer(s): (a) 30 : 3 : 1; (b) 66 cm
2