The rectangle is divided into four parts H, J, K and L. The ratio of Part H to Part J is 9 : 2 and the ratio of Part J to Part K is 3 : 1.
- Find the ratio of Part H to Part J to Part K.
- Given that Part L is 62 m2 , find the area of the rectangle.
(a)
H |
J |
K |
L |
9x3 |
2x3 |
|
|
|
3x2 |
1x2 |
|
27 u |
6 u |
2 u |
62 m2 |
Part J is the repeated identity.
LCM of 2 and 3 = 6
Part H : Part J : Part K = 27 : 6 : 2
(b)
Part H + Part J = Half of the rectangle
Part K + Part L = Half of the rectangle
Part H + Part J and Part K + Part L are equal.
Part H + Part J = Part K + Part L
27 u + 6 u = 2 u + 62
27 u + 6 u - 2 u = 62
31 u = 62
1 u = 62 ÷ 31 = 2
Area of the rectangle
= 2 x (2 u + 62)
= 2 x (2 x 2 + 62)
= 2 x (4 + 62)
= 2 x 66
= 132 m
2 Answer(s): (a) 27 : 6 : 2; (b) 132 m
2