The rectangle is divided into four parts N, P, Q and R. The ratio of Part N to Part P is 6 : 5 and the ratio of Part P to Part Q is 3 : 2.
- Find the ratio of Part N to Part P to Part Q.
- Given that Part R is 69 cm2 , find the area of the rectangle.
(a)
N |
P |
Q |
R |
6x3 |
5x3 |
|
|
|
3x5 |
2x5 |
|
18 u |
15 u |
10 u |
69 cm2 |
Part P is the repeated identity.
LCM of 5 and 3 = 15
Part N : Part P : Part Q = 18 : 15 : 10
(b)
Part N + Part P = Half of the rectangle
Part Q + Part R = Half of the rectangle
Part N + Part P and Part Q + Part R are equal.
Part N + Part P = Part Q + Part R
18 u + 15 u = 10 u + 69
18 u + 15 u - 10 u = 69
23 u = 69
1 u = 69 ÷ 23 = 3
Area of the rectangle
= 2 x (10 u + 69)
= 2 x (10 x 3 + 69)
= 2 x (30 + 69)
= 2 x 99
= 198 cm
2 Answer(s): (a) 18 : 15 : 10; (b) 198 cm
2