The rectangle is divided into four parts N, P, Q and R. The ratio of Part N to Part P is 9 : 2 and the ratio of Part P to Part Q is 4 : 1.
- Find the ratio of Part N to Part P to Part Q.
- Given that Part R is 63 cm2 , find the area of the rectangle.
(a)
N |
P |
Q |
R |
9x2 |
2x2 |
|
|
|
4x1 |
1x1 |
|
18 u |
4 u |
1 u |
63 cm2 |
Part P is the repeated identity.
LCM of 2 and 4 = 4
Part N : Part P : Part Q = 18 : 4 : 1
(b)
Part N + Part P = Half of the rectangle
Part Q + Part R = Half of the rectangle
Part N + Part P and Part Q + Part R are equal.
Part N + Part P = Part Q + Part R
18 u + 4 u = 1 u + 63
18 u + 4 u - 1 u = 63
21 u = 63
1 u = 63 ÷ 21 = 3
Area of the rectangle
= 2 x (1 u + 63)
= 2 x (1 x 3 + 63)
= 2 x (3 + 63)
= 2 x 66
= 132 cm
2 Answer(s): (a) 18 : 4 : 1; (b) 132 cm
2