The rectangle is divided into four parts W, X, Y and Z. The ratio of Part W to Part X is 7 : 4 and the ratio of Part X to Part Y is 3 : 1.
- Find the ratio of Part W to Part X to Part Y.
- Given that Part Z is 58 cm2 , find the area of the rectangle.
(a)
W |
X |
Y |
Z |
7x3 |
4x3 |
|
|
|
3x4 |
1x4 |
|
21 u |
12 u |
4 u |
58 cm2 |
Part X is the repeated identity.
LCM of 4 and 3 = 12
Part W : Part X : Part Y = 21 : 12 : 4
(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
21 u + 12 u = 4 u + 58
21 u + 12 u - 4 u = 58
29 u = 58
1 u = 58 ÷ 29 = 2
Area of the rectangle
= 2 x (4 u + 58)
= 2 x (4 x 2 + 58)
= 2 x (8 + 58)
= 2 x 66
= 132 cm
2 Answer(s): (a) 21 : 12 : 4; (b) 132 cm
2