The rectangle is divided into four parts D, E, F and G. The ratio of Part D to Part E is 7 : 3 and the ratio of Part E to Part F is 3 : 2.
- Find the ratio of Part D to Part E to Part F.
- Given that Part G is 16 cm2 , find the area of the rectangle.
(a)
D |
E |
F |
G |
7x1 |
3x1 |
|
|
|
3x1 |
2x1 |
|
7 u |
3 u |
2 u |
16 cm2 |
Part E is the repeated identity.
LCM of 3 and 3 = 3
Part D : Part E : Part F = 7 : 3 : 2
(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 + 3 u = 2 u + 16
7 u + 3 u - 2 u = 16
8 u = 16
1 u = 16 ÷ 8 = 2
Area of the rectangle
= 2 x (2 u + 16)
= 2 x (2 x 2 + 16)
= 2 x (4 + 16)
= 2 x 20
= 40 cm
2 Answer(s): (a) 7 : 3 : 2; (b) 40 cm
2