The rectangle is divided into four parts C, D, E and F. The ratio of Part C to Part D is 10 : 3 and the ratio of Part D to Part E is 3 : 2.
- Find the ratio of Part C to Part D to Part E.
- Given that Part F is 66 m2 , find the area of the rectangle.
(a)
C |
D |
E |
F |
10x1 |
3x1 |
|
|
|
3x1 |
2x1 |
|
10 u |
3 u |
2 u |
66 m2 |
Part D is the repeated identity.
LCM of 3 and 3 = 3
Part C : Part D : Part E = 10 : 3 : 2
(b)
Part C + Part D = Half of the rectangle
Part E + Part F = Half of the rectangle
Part C + Part D and Part E + Part F are equal.
Part C + Part D = Part E + Part F
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 m
2 Answer(s): (a) 10 : 3 : 2; (b) 156 m
2