The rectangle is divided into four parts N, P, Q and R. The ratio of Part N to Part P is 9 : 4 and the ratio of Part P to Part Q is 4 : 1.
- Find the ratio of Part N to Part P to Part Q.
- Given that Part R is 72 cm2 , find the area of the rectangle.
(a)
N |
P |
Q |
R |
9x1 |
4x1 |
|
|
|
4x1 |
1x1 |
|
9 u |
4 u |
1 u |
72 cm2 |
Part P is the repeated identity.
LCM of 4 and 4 = 4
Part N : Part P : Part Q = 9 : 4 : 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
9 u + 4 u = 1 u + 72
9 u + 4 u - 1 u = 72
12 u = 72
1 u = 72 ÷ 12 = 6
Area of the rectangle
= 2 x (1 u + 72)
= 2 x (1 x 6 + 72)
= 2 x (6 + 72)
= 2 x 78
= 156 cm
2 Answer(s): (a) 9 : 4 : 1; (b) 156 cm
2