The rectangle is divided into four parts E, F, G and H. The ratio of Part E to Part F is 7 : 3 and the ratio of Part F to Part G is 3 : 2.
- Find the ratio of Part E to Part F to Part G.
- Given that Part H is 40 m2 , find the area of the rectangle.
(a)
E |
F |
G |
H |
7x1 |
3x1 |
|
|
|
3x1 |
2x1 |
|
7 u |
3 u |
2 u |
40 m2 |
Part F is the repeated identity.
LCM of 3 and 3 = 3
Part E : Part F : Part G = 7 : 3 : 2
(b)
Part E + Part F = Half of the rectangle
Part G + Part H = Half of the rectangle
Part E + Part F and Part G + Part H are equal.
Part E + Part F = Part G + Part H
7 u + 3 u = 2 u + 40
7 u + 3 u - 2 u = 40
8 u = 40
1 u = 40 ÷ 8 = 5
Area of the rectangle
= 2 x (2 u + 40)
= 2 x (2 x 5 + 40)
= 2 x (10 + 40)
= 2 x 50
= 100 m
2 Answer(s): (a) 7 : 3 : 2; (b) 100 m
2