The rectangle is divided into four parts W, X, Y and Z. The ratio of Part W to Part X is 10 : 3 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 99 m2 , find the area of the rectangle.
(a)
W |
X |
Y |
Z |
10x1 |
3x1 |
|
|
|
3x1 |
2x1 |
|
10 u |
3 u |
2 u |
99 m2 |
Part X is the repeated identity.
LCM of 3 and 3 = 3
Part W : Part X : Part Y = 10 : 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
10 u + 3 u = 2 u + 99
10 u + 3 u - 2 u = 99
11 u = 99
1 u = 99 ÷ 11 = 9
Area of the rectangle
= 2 x (2 u + 99)
= 2 x (2 x 9 + 99)
= 2 x (18 + 99)
= 2 x 117
= 234 m
2 Answer(s): (a) 10 : 3 : 2; (b) 234 m
2