The rectangle is divided into four parts D, E, F and G. The ratio of Part D to Part E is 7 : 4 and the ratio of Part E to Part F is 4 : 1.
- Find the ratio of Part D to Part E to Part F.
- Given that Part G is 20 cm2 , find the area of the rectangle.
(a)
D |
E |
F |
G |
7x1 |
4x1 |
|
|
|
4x1 |
1x1 |
|
7 u |
4 u |
1 u |
20 cm2 |
Part E is the repeated identity.
LCM of 4 and 4 = 4
Part D : Part E : Part F = 7 : 4 : 1
(b)
Part D + Part E = Half of the rectangle
Part F + Part G = Half of the rectangle
Part D + Part E and Part F + Part G are equal.
Part D + Part E = Part F + Part G
7 u + 4 u = 1 u + 20
7 u + 4 u - 1 u = 20
10 u = 20
1 u = 20 ÷ 10 = 2
Area of the rectangle
= 2 x (1 u + 20)
= 2 x (1 x 2 + 20)
= 2 x (2 + 20)
= 2 x 22
= 44 cm
2 Answer(s): (a) 7 : 4 : 1; (b) 44 cm
2