The rectangle is divided into four parts N, P, Q and R. The ratio of Part N to Part P is 7 : 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 27 cm2 , find the area of the rectangle.
(a)
N |
P |
Q |
R |
7x1 |
3x1 |
|
|
|
3x1 |
1x1 |
|
7 u |
3 u |
1 u |
27 cm2 |
Part P is the repeated identity.
LCM of 3 and 3 = 3
Part N : Part P : Part Q = 7 : 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
7 u + 3 u = 1 u + 27
7 u + 3 u - 1 u = 27
9 u = 27
1 u = 27 ÷ 9 = 3
Area of the rectangle
= 2 x (1 u + 27)
= 2 x (1 x 3 + 27)
= 2 x (3 + 27)
= 2 x 30
= 60 cm
2 Answer(s): (a) 7 : 3 : 1; (b) 60 cm
2