The rectangle is divided into four parts D, E, F and G. The ratio of Part D to Part E is 10 : 3 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 24 m2 , find the area of the rectangle.
(a)
D |
E |
F |
G |
10x1 |
3x1 |
|
|
|
3x1 |
1x1 |
|
10 u |
3 u |
1 u |
24 m2 |
Part E is the repeated identity.
LCM of 3 and 3 = 3
Part D : Part E : Part F = 10 : 3 : 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
10 u + 3 u = 1 u + 24
10 u + 3 u - 1 u = 24
12 u = 24
1 u = 24 ÷ 12 = 2
Area of the rectangle
= 2 x (1 u + 24)
= 2 x (1 x 2 + 24)
= 2 x (2 + 24)
= 2 x 26
= 52 m
2 Answer(s): (a) 10 : 3 : 1; (b) 52 m
2