The rectangle is divided into four parts P, Q, R and S. The ratio of Part P to Part Q is 7 : 4 and the ratio of Part Q to Part R is 3 : 2.
- Find the ratio of Part P to Part Q to Part R.
- Given that Part S is 75 cm2 , find the area of the rectangle.
(a)
P |
Q |
R |
S |
7x3 |
4x3 |
|
|
|
3x4 |
2x4 |
|
21 u |
12 u |
8 u |
75 cm2 |
Part Q is the repeated identity.
LCM of 4 and 3 = 12
Part P : Part Q : Part R = 21 : 12 : 8
(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
21 u + 12 u = 8 u + 75
21 u + 12 u - 8 u = 75
25 u = 75
1 u = 75 ÷ 25 = 3
Area of the rectangle
= 2 x (8 u + 75)
= 2 x (8 x 3 + 75)
= 2 x (24 + 75)
= 2 x 99
= 198 cm
2 Answer(s): (a) 21 : 12 : 8; (b) 198 cm
2