The rectangle is divided into four parts M, N, P and Q. The ratio of Part M to Part N is 9 : 4 and the ratio of Part N to Part P is 3 : 2.
- Find the ratio of Part M to Part N to Part P.
- Given that Part Q is 62 m2 , find the area of the rectangle.
(a)
M |
N |
P |
Q |
9x3 |
4x3 |
|
|
|
3x4 |
2x4 |
|
27 u |
12 u |
8 u |
62 m2 |
Part N is the repeated identity.
LCM of 4 and 3 = 12
Part M : Part N : Part P = 27 : 12 : 8
(b)
Part M + Part N = Half of the rectangle
Part P + Part Q = Half of the rectangle
Part M + Part N and Part P + Part Q are equal.
Part M + Part N = Part P + Part Q
27 u + 12 u = 8 u + 62
27 u + 12 u - 8 u = 62
31 u = 62
1 u = 62 ÷ 31 = 2
Area of the rectangle
= 2 x (8 u + 62)
= 2 x (8 x 2 + 62)
= 2 x (16 + 62)
= 2 x 78
= 156 m
2 Answer(s): (a) 27 : 12 : 8; (b) 156 m
2