The rectangle is divided into four parts N, P, Q and R. The ratio of Part N to Part P is 8 : 3 and the ratio of Part P to Part Q is 3 : 1.
- Find the ratio of Part N to Part P to Part Q.
- Given that Part R is 30 m2 , find the area of the rectangle.
(a)
N |
P |
Q |
R |
8x1 |
3x1 |
|
|
|
3x1 |
1x1 |
|
8 u |
3 u |
1 u |
30 m2 |
Part P is the repeated identity.
LCM of 3 and 3 = 3
Part N : Part P : Part Q = 8 : 3 : 1
(b)
Part N + Part P = Half of the rectangle
Part Q + Part R = Half of the rectangle
Part N + Part P and Part Q + Part R are equal.
Part N + Part P = Part Q + Part R
8 u + 3 u = 1 u + 30
8 u + 3 u - 1 u = 30
10 u = 30
1 u = 30 ÷ 10 = 3
Area of the rectangle
= 2 x (1 u + 30)
= 2 x (1 x 3 + 30)
= 2 x (3 + 30)
= 2 x 33
= 66 m
2 Answer(s): (a) 8 : 3 : 1; (b) 66 m
2