The rectangle is divided into four parts Y, Z, A and B. The ratio of Part Y to Part Z is 7 : 3 and the ratio of Part Z to Part A is 3 : 1.
- Find the ratio of Part Y to Part Z to Part A.
- Given that Part B is 63 cm2 , find the area of the rectangle.
(a)
Y |
Z |
A |
B |
7x1 |
3x1 |
|
|
|
3x1 |
1x1 |
|
7 u |
3 u |
1 u |
63 cm2 |
Part Z is the repeated identity.
LCM of 3 and 3 = 3
Part Y : Part Z : Part A = 7 : 3 : 1
(b)
Part Y + Part Z = Half of the rectangle
Part A + Part B = Half of the rectangle
Part Y + Part Z and Part A + Part B are equal.
Part Y + Part Z = Part A + Part B
7 u + 3 u = 1 u + 63
7 u + 3 u - 1 u = 63
9 u = 63
1 u = 63 ÷ 9 = 7
Area of the rectangle
= 2 x (1 u + 63)
= 2 x (1 x 7 + 63)
= 2 x (7 + 63)
= 2 x 70
= 140 cm
2 Answer(s): (a) 7 : 3 : 1; (b) 140 cm
2