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 4 : 1.
- Find the ratio of Part P to Part Q to Part R.
- Given that Part S is 60 m2 , find the area of the rectangle.
(a)
P |
Q |
R |
S |
7x1 |
4x1 |
|
|
|
4x1 |
1x1 |
|
7 u |
4 u |
1 u |
60 m2 |
Part Q is the repeated identity.
LCM of 4 and 4 = 4
Part P : Part Q : Part R = 7 : 4 : 1
(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
7 u + 4 u = 1 u + 60
7 u + 4 u - 1 u = 60
10 u = 60
1 u = 60 ÷ 10 = 6
Area of the rectangle
= 2 x (1 u + 60)
= 2 x (1 x 6 + 60)
= 2 x (6 + 60)
= 2 x 66
= 132 m
2 Answer(s): (a) 7 : 4 : 1; (b) 132 m
2