The rectangle is divided into four parts Q, R, S and T. The ratio of Part Q to Part R is 7 : 4 and the ratio of Part R to Part S is 4 : 1.
- Find the ratio of Part Q to Part R to Part S.
- Given that Part T is 40 m2 , find the area of the rectangle.
(a)
Q |
R |
S |
T |
7x1 |
4x1 |
|
|
|
4x1 |
1x1 |
|
7 u |
4 u |
1 u |
40 m2 |
Part R is the repeated identity.
LCM of 4 and 4 = 4
Part Q : Part R : Part S = 7 : 4 : 1
(b)
Part Q + Part R = Half of the rectangle
Part S + Part T = Half of the rectangle
Part Q + Part R and Part S + Part T are equal.
Part Q + Part R = Part S + Part T
7 u + 4 u = 1 u + 40
7 u + 4 u - 1 u = 40
10 u = 40
1 u = 40 ÷ 10 = 4
Area of the rectangle
= 2 x (1 u + 40)
= 2 x (1 x 4 + 40)
= 2 x (4 + 40)
= 2 x 44
= 88 m
2 Answer(s): (a) 7 : 4 : 1; (b) 88 m
2