The rectangle is divided into four parts Y, Z, A and B. The ratio of Part Y to Part Z is 7 : 5 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 31 cm2 , find the area of the rectangle.
(a)
Y |
Z |
A |
B |
7x3 |
5x3 |
|
|
|
3x5 |
1x5 |
|
21 u |
15 u |
5 u |
31 cm2 |
Part Z is the repeated identity.
LCM of 5 and 3 = 15
Part Y : Part Z : Part A = 21 : 15 : 5
(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
21 u + 15 u = 5 u + 31
21 u + 15 u - 5 u = 31
31 u = 31
1 u = 31 ÷ 31 = 1
Area of the rectangle
= 2 x (5 u + 31)
= 2 x (5 x 1 + 31)
= 2 x (5 + 31)
= 2 x 36
= 72 cm
2 Answer(s): (a) 21 : 15 : 5; (b) 72 cm
2