The rectangle is divided into four parts N, P, Q and R. The ratio of Part N to Part P is 9 : 5 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 51 m2 , find the area of the rectangle.
(a)
N |
P |
Q |
R |
9x4 |
5x4 |
|
|
|
4x5 |
1x5 |
|
36 u |
20 u |
5 u |
51 m2 |
Part P is the repeated identity.
LCM of 5 and 4 = 20
Part N : Part P : Part Q = 36 : 20 : 5
(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
36 u + 20 u = 5 u + 51
36 u + 20 u - 5 u = 51
51 u = 51
1 u = 51 ÷ 51 = 1
Area of the rectangle
= 2 x (5 u + 51)
= 2 x (5 x 1 + 51)
= 2 x (5 + 51)
= 2 x 56
= 112 m
2 Answer(s): (a) 36 : 20 : 5; (b) 112 m
2