The rectangle is divided into four parts M, N, P and Q. The ratio of Part M to Part N is 10 : 1 and the ratio of Part N to Part P is 4 : 1.
- Find the ratio of Part M to Part N to Part P.
- Given that Part Q is 43 cm2 , find the area of the rectangle.
(a)
M |
N |
P |
Q |
10x4 |
1x4 |
|
|
|
4x1 |
1x1 |
|
40 u |
4 u |
1 u |
43 cm2 |
Part N is the repeated identity.
LCM of 1 and 4 = 4
Part M : Part N : Part P = 40 : 4 : 1
(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
40 u + 4 u = 1 u + 43
40 u + 4 u - 1 u = 43
43 u = 43
1 u = 43 ÷ 43 = 1
Area of the rectangle
= 2 x (1 u + 43)
= 2 x (1 x 1 + 43)
= 2 x (1 + 43)
= 2 x 44
= 88 cm
2 Answer(s): (a) 40 : 4 : 1; (b) 88 cm
2