The rectangle is divided into four parts W, X, Y and Z. The ratio of Part W to Part X is 6 : 5 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 23 cm2 , find the area of the rectangle.
(a)
W |
X |
Y |
Z |
6x3 |
5x3 |
|
|
|
3x5 |
2x5 |
|
18 u |
15 u |
10 u |
23 cm2 |
Part X is the repeated identity.
LCM of 5 and 3 = 15
Part W : Part X : Part Y = 18 : 15 : 10
(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
18 u + 15 u = 10 u + 23
18 u + 15 u - 10 u = 23
23 u = 23
1 u = 23 ÷ 23 = 1
Area of the rectangle
= 2 x (10 u + 23)
= 2 x (10 x 1 + 23)
= 2 x (10 + 23)
= 2 x 33
= 66 cm
2 Answer(s): (a) 18 : 15 : 10; (b) 66 cm
2