The rectangle is divided into four parts V, W, X and Y. The ratio of Part V to Part W is 7 : 4 and the ratio of Part W to Part X is 3 : 1.
- Find the ratio of Part V to Part W to Part X.
- Given that Part Y is 87 m2 , find the area of the rectangle.
(a)
V |
W |
X |
Y |
7x3 |
4x3 |
|
|
|
3x4 |
1x4 |
|
21 u |
12 u |
4 u |
87 m2 |
Part W is the repeated identity.
LCM of 4 and 3 = 12
Part V : Part W : Part X = 21 : 12 : 4
(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
21 u + 12 u = 4 u + 87
21 u + 12 u - 4 u = 87
29 u = 87
1 u = 87 ÷ 29 = 3
Area of the rectangle
= 2 x (4 u + 87)
= 2 x (4 x 3 + 87)
= 2 x (12 + 87)
= 2 x 99
= 198 m
2 Answer(s): (a) 21 : 12 : 4; (b) 198 m
2