The rectangle is divided into four parts E, F, G and H. The ratio of Part E to Part F is 10 : 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 77 m2 , find the area of the rectangle.
(a)
E |
F |
G |
H |
10x1 |
3x1 |
|
|
|
3x1 |
2x1 |
|
10 u |
3 u |
2 u |
77 m2 |
Part F is the repeated identity.
LCM of 3 and 3 = 3
Part E : Part F : Part G = 10 : 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
10 u + 3 u = 2 u + 77
10 u + 3 u - 2 u = 77
11 u = 77
1 u = 77 ÷ 11 = 7
Area of the rectangle
= 2 x (2 u + 77)
= 2 x (2 x 7 + 77)
= 2 x (14 + 77)
= 2 x 91
= 182 m
2 Answer(s): (a) 10 : 3 : 2; (b) 182 m
2