The rectangle is divided into four parts S, T, U and V. The ratio of Part S to Part T is 6 : 5 and the ratio of Part T to Part U is 4 : 1.
- Find the ratio of Part S to Part T to Part U.
- Given that Part V is 78 m2 , find the area of the rectangle.
(a)
S |
T |
U |
V |
6x4 |
5x4 |
|
|
|
4x5 |
1x5 |
|
24 u |
20 u |
5 u |
78 m2 |
Part T is the repeated identity.
LCM of 5 and 4 = 20
Part S : Part T : Part U = 24 : 20 : 5
(b)
Part S + Part T = Half of the rectangle
Part U + Part V = Half of the rectangle
Part S + Part T and Part U + Part V are equal.
Part S + Part T = Part U + Part V
24 u + 20 u = 5 u + 78
24 u + 20 u - 5 u = 78
39 u = 78
1 u = 78 ÷ 39 = 2
Area of the rectangle
= 2 x (5 u + 78)
= 2 x (5 x 2 + 78)
= 2 x (10 + 78)
= 2 x 88
= 176 m
2 Answer(s): (a) 24 : 20 : 5; (b) 176 m
2