The rectangle is divided into four parts L, M, N and P. The ratio of Part L to Part M is 9 : 4 and the ratio of Part M to Part N is 4 : 1.
- Find the ratio of Part L to Part M to Part N.
- Given that Part P is 36 m2 , find the area of the rectangle.
(a)
L |
M |
N |
P |
9x1 |
4x1 |
|
|
|
4x1 |
1x1 |
|
9 u |
4 u |
1 u |
36 m2 |
Part M is the repeated identity.
LCM of 4 and 4 = 4
Part L : Part M : Part N = 9 : 4 : 1
(b)
Part L + Part M = Half of the rectangle
Part N + Part P = Half of the rectangle
Part L + Part M and Part N + Part P are equal.
Part L + Part M = Part N + Part P
9 u + 4 u = 1 u + 36
9 u + 4 u - 1 u = 36
12 u = 36
1 u = 36 ÷ 12 = 3
Area of the rectangle
= 2 x (1 u + 36)
= 2 x (1 x 3 + 36)
= 2 x (3 + 36)
= 2 x 39
= 78 m
2 Answer(s): (a) 9 : 4 : 1; (b) 78 m
2