The rectangle is divided into four parts W, X, Y and Z. The ratio of Part W to Part X is 7 : 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 80 cm2 , find the area of the rectangle.
(a)
W |
X |
Y |
Z |
7x1 |
3x1 |
|
|
|
3x1 |
2x1 |
|
7 u |
3 u |
2 u |
80 cm2 |
Part X is the repeated identity.
LCM of 3 and 3 = 3
Part W : Part X : Part Y = 7 : 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
7 u + 3 u = 2 u + 80
7 u + 3 u - 2 u = 80
8 u = 80
1 u = 80 ÷ 8 = 10
Area of the rectangle
= 2 x (2 u + 80)
= 2 x (2 x 10 + 80)
= 2 x (20 + 80)
= 2 x 100
= 200 cm
2 Answer(s): (a) 7 : 3 : 2; (b) 200 cm
2