The rectangle is divided into four parts D, E, F and G. The ratio of Part D to Part E is 7 : 5 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 62 m2 , find the area of the rectangle.
(a)
D |
E |
F |
G |
7x3 |
5x3 |
|
|
|
3x5 |
1x5 |
|
21 u |
15 u |
5 u |
62 m2 |
Part E is the repeated identity.
LCM of 5 and 3 = 15
Part D : Part E : Part F = 21 : 15 : 5
(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
21 u + 15 u = 5 u + 62
21 u + 15 u - 5 u = 62
31 u = 62
1 u = 62 ÷ 31 = 2
Area of the rectangle
= 2 x (5 u + 62)
= 2 x (5 x 2 + 62)
= 2 x (10 + 62)
= 2 x 72
= 144 m
2 Answer(s): (a) 21 : 15 : 5; (b) 144 m
2