The rectangle is divided into four parts C, D, E and F. The ratio of Part C to Part D is 7 : 3 and the ratio of Part D to Part E is 3 : 1.
- Find the ratio of Part C to Part D to Part E.
- Given that Part F is 54 cm2 , find the area of the rectangle.
(a)
C |
D |
E |
F |
7x1 |
3x1 |
|
|
|
3x1 |
1x1 |
|
7 u |
3 u |
1 u |
54 cm2 |
Part D is the repeated identity.
LCM of 3 and 3 = 3
Part C : Part D : Part E = 7 : 3 : 1
(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
7 u + 3 u = 1 u + 54
7 u + 3 u - 1 u = 54
9 u = 54
1 u = 54 ÷ 9 = 6
Area of the rectangle
= 2 x (1 u + 54)
= 2 x (1 x 6 + 54)
= 2 x (6 + 54)
= 2 x 60
= 120 cm
2 Answer(s): (a) 7 : 3 : 1; (b) 120 cm
2