The rectangle is divided into four parts W, X, Y and Z. The ratio of Part W to Part X is 10 : 1 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 93 m2 , find the area of the rectangle.
(a)
W |
X |
Y |
Z |
10x3 |
1x3 |
|
|
|
3x1 |
2x1 |
|
30 u |
3 u |
2 u |
93 m2 |
Part X is the repeated identity.
LCM of 1 and 3 = 3
Part W : Part X : Part Y = 30 : 3 : 2
(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
30 u + 3 u = 2 u + 93
30 u + 3 u - 2 u = 93
31 u = 93
1 u = 93 ÷ 31 = 3
Area of the rectangle
= 2 x (2 u + 93)
= 2 x (2 x 3 + 93)
= 2 x (6 + 93)
= 2 x 99
= 198 m
2 Answer(s): (a) 30 : 3 : 2; (b) 198 m
2