The rectangle is divided into four parts M, N, P and Q. The ratio of Part M to Part N is 10 : 3 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 77 cm2 , find the area of the rectangle.
(a)
M |
N |
P |
Q |
10x1 |
3x1 |
|
|
|
3x1 |
2x1 |
|
10 u |
3 u |
2 u |
77 cm2 |
Part N is the repeated identity.
LCM of 3 and 3 = 3
Part M : Part N : Part P = 10 : 3 : 2
(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
10 u + 3 u = 2 u + 77
10 u + 3 u - 2 u = 77
11 u = 77
1 u = 77 ÷ 11 = 7
Area of the rectangle
= 2 x (2 u + 77)
= 2 x (2 x 7 + 77)
= 2 x (14 + 77)
= 2 x 91
= 182 cm
2 Answer(s): (a) 10 : 3 : 2; (b) 182 cm
2