The rectangle is divided into four parts L, M, N and P. The ratio of Part L to Part M is 6 : 1 and the ratio of Part M to Part N is 3 : 2.
- Find the ratio of Part L to Part M to Part N.
- Given that Part P is 57 cm2 , find the area of the rectangle.
(a)
L |
M |
N |
P |
6x3 |
1x3 |
|
|
|
3x1 |
2x1 |
|
18 u |
3 u |
2 u |
57 cm2 |
Part M is the repeated identity.
LCM of 1 and 3 = 3
Part L : Part M : Part N = 18 : 3 : 2
(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
18 u + 3 u = 2 u + 57
18 u + 3 u - 2 u = 57
19 u = 57
1 u = 57 ÷ 19 = 3
Area of the rectangle
= 2 x (2 u + 57)
= 2 x (2 x 3 + 57)
= 2 x (6 + 57)
= 2 x 63
= 126 cm
2 Answer(s): (a) 18 : 3 : 2; (b) 126 cm
2