The rectangle is divided into four parts P, Q, R and S. The ratio of Part P to Part Q is 7 : 2 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 23 m2 , find the area of the rectangle.
(a)
P |
Q |
R |
S |
7x3 |
2x3 |
|
|
|
3x2 |
2x2 |
|
21 u |
6 u |
4 u |
23 m2 |
Part Q is the repeated identity.
LCM of 2 and 3 = 6
Part P : Part Q : Part R = 21 : 6 : 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 + 6 u = 4 u + 23
21 u + 6 u - 4 u = 23
23 u = 23
1 u = 23 ÷ 23 = 1
Area of the rectangle
= 2 x (4 u + 23)
= 2 x (4 x 1 + 23)
= 2 x (4 + 23)
= 2 x 27
= 54 m
2 Answer(s): (a) 21 : 6 : 4; (b) 54 m
2