The rectangle is divided into four parts D, E, F and G. The ratio of Part D to Part E is 9 : 5 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 64 cm2 , find the area of the rectangle.
(a)
D |
E |
F |
G |
9x3 |
5x3 |
|
|
|
3x5 |
2x5 |
|
27 u |
15 u |
10 u |
64 cm2 |
Part E is the repeated identity.
LCM of 5 and 3 = 15
Part D : Part E : Part F = 27 : 15 : 10
(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 + 15 u = 10 u + 64
27 u + 15 u - 10 u = 64
32 u = 64
1 u = 64 ÷ 32 = 2
Area of the rectangle
= 2 x (10 u + 64)
= 2 x (10 x 2 + 64)
= 2 x (20 + 64)
= 2 x 84
= 168 cm
2 Answer(s): (a) 27 : 15 : 10; (b) 168 cm
2