The rectangle is divided into four parts C, D, E and F. The ratio of Part C to Part D is 7 : 4 and the ratio of Part D to Part E is 4 : 1.
- Find the ratio of Part C to Part D to Part E.
- Given that Part F is 80 cm2 , find the area of the rectangle.
(a)
C |
D |
E |
F |
7x1 |
4x1 |
|
|
|
4x1 |
1x1 |
|
7 u |
4 u |
1 u |
80 cm2 |
Part D is the repeated identity.
LCM of 4 and 4 = 4
Part C : Part D : Part E = 7 : 4 : 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 + 4 u = 1 u + 80
7 u + 4 u - 1 u = 80
10 u = 80
1 u = 80 ÷ 10 = 8
Area of the rectangle
= 2 x (1 u + 80)
= 2 x (1 x 8 + 80)
= 2 x (8 + 80)
= 2 x 88
= 176 cm
2 Answer(s): (a) 7 : 4 : 1; (b) 176 cm
2