The rectangle is divided into four parts V, W, X and Y. The ratio of Part V to Part W is 6 : 1 and the ratio of Part W to Part X is 4 : 1.
- Find the ratio of Part V to Part W to Part X.
- Given that Part Y is 27 m2 , find the area of the rectangle.
(a)
V |
W |
X |
Y |
6x4 |
1x4 |
|
|
|
4x1 |
1x1 |
|
24 u |
4 u |
1 u |
27 m2 |
Part W is the repeated identity.
LCM of 1 and 4 = 4
Part V : Part W : Part X = 24 : 4 : 1
(b)
Part V + Part W = Half of the rectangle
Part X + Part Y = Half of the rectangle
Part V + Part W and Part X + Part Y are equal.
Part V + Part W = Part X + Part Y
24 u + 4 u = 1 u + 27
24 u + 4 u - 1 u = 27
27 u = 27
1 u = 27 ÷ 27 = 1
Area of the rectangle
= 2 x (1 u + 27)
= 2 x (1 x 1 + 27)
= 2 x (1 + 27)
= 2 x 28
= 56 m
2 Answer(s): (a) 24 : 4 : 1; (b) 56 m
2