The rectangle is divided into four parts P, Q, R and S. The ratio of Part P to Part Q is 6 : 5 and the ratio of Part Q to Part R is 3 : 1.
- Find the ratio of Part P to Part Q to Part R.
- Given that Part S is 84 m2 , find the area of the rectangle.
(a)
P |
Q |
R |
S |
6x3 |
5x3 |
|
|
|
3x5 |
1x5 |
|
18 u |
15 u |
5 u |
84 m2 |
Part Q is the repeated identity.
LCM of 5 and 3 = 15
Part P : Part Q : Part R = 18 : 15 : 5
(b)
Part P + Part Q = Half of the rectangle
Part R + Part S = Half of the rectangle
Part P + Part Q and Part R + Part S are equal.
Part P + Part Q = Part R + Part S
18 u + 15 u = 5 u + 84
18 u + 15 u - 5 u = 84
28 u = 84
1 u = 84 ÷ 28 = 3
Area of the rectangle
= 2 x (5 u + 84)
= 2 x (5 x 3 + 84)
= 2 x (15 + 84)
= 2 x 99
= 198 m
2 Answer(s): (a) 18 : 15 : 5; (b) 198 m
2