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 : 1.
- Find the ratio of Part P to Part Q to Part R.
- Given that Part S is 29 cm2 , find the area of the rectangle.
(a)
P |
Q |
R |
S |
7x3 |
4x3 |
|
|
|
3x4 |
1x4 |
|
21 u |
12 u |
4 u |
29 cm2 |
Part Q is the repeated identity.
LCM of 4 and 3 = 12
Part P : Part Q : Part R = 21 : 12 : 4
(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 = 4 u + 29
21 u + 12 u - 4 u = 29
29 u = 29
1 u = 29 ÷ 29 = 1
Area of the rectangle
= 2 x (4 u + 29)
= 2 x (4 x 1 + 29)
= 2 x (4 + 29)
= 2 x 33
= 66 cm
2 Answer(s): (a) 21 : 12 : 4; (b) 66 cm
2