The rectangle is divided into four parts W, X, Y and Z. The ratio of Part W to Part X is 7 : 2 and the ratio of Part X to Part Y is 3 : 2.
- Find the ratio of Part W to Part X to Part Y.
- Given that Part Z is 46 m2 , find the area of the rectangle.
(a)
W |
X |
Y |
Z |
7x3 |
2x3 |
|
|
|
3x2 |
2x2 |
|
21 u |
6 u |
4 u |
46 m2 |
Part X is the repeated identity.
LCM of 2 and 3 = 6
Part W : Part X : Part Y = 21 : 6 : 4
(b)
Part W + Part X = Half of the rectangle
Part Y + Part Z = Half of the rectangle
Part W + Part X and Part Y + Part Z are equal.
Part W + Part X = Part Y + Part Z
21 u + 6 u = 4 u + 46
21 u + 6 u - 4 u = 46
23 u = 46
1 u = 46 ÷ 23 = 2
Area of the rectangle
= 2 x (4 u + 46)
= 2 x (4 x 2 + 46)
= 2 x (8 + 46)
= 2 x 54
= 108 m
2 Answer(s): (a) 21 : 6 : 4; (b) 108 m
2