The rectangle is divided into four parts D, E, F and G. The ratio of Part D to Part E is 9 : 4 and the ratio of Part E to Part F is 3 : 1.
- Find the ratio of Part D to Part E to Part F.
- Given that Part G is 35 cm2 , find the area of the rectangle.
(a)
D |
E |
F |
G |
9x3 |
4x3 |
|
|
|
3x4 |
1x4 |
|
27 u |
12 u |
4 u |
35 cm2 |
Part E is the repeated identity.
LCM of 4 and 3 = 12
Part D : Part E : Part F = 27 : 12 : 4
(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
27 u + 12 u = 4 u + 35
27 u + 12 u - 4 u = 35
35 u = 35
1 u = 35 ÷ 35 = 1
Area of the rectangle
= 2 x (4 u + 35)
= 2 x (4 x 1 + 35)
= 2 x (4 + 35)
= 2 x 39
= 78 cm
2 Answer(s): (a) 27 : 12 : 4; (b) 78 cm
2