The rectangle is divided into four parts K, L, M and N. The ratio of Part K to Part L is 8 : 5 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 68 cm2 , find the area of the rectangle.
(a)
K |
L |
M |
N |
8x3 |
5x3 |
|
|
|
3x5 |
1x5 |
|
24 u |
15 u |
5 u |
68 cm2 |
Part L is the repeated identity.
LCM of 5 and 3 = 15
Part K : Part L : Part M = 24 : 15 : 5
(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 + 15 u = 5 u + 68
24 u + 15 u - 5 u = 68
34 u = 68
1 u = 68 ÷ 34 = 2
Area of the rectangle
= 2 x (5 u + 68)
= 2 x (5 x 2 + 68)
= 2 x (10 + 68)
= 2 x 78
= 156 cm
2 Answer(s): (a) 24 : 15 : 5; (b) 156 cm
2