The rectangle is divided into four parts H, J, K and L. The ratio of Part H to Part J is 9 : 5 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 37 cm2 , find the area of the rectangle.
(a)
H |
J |
K |
L |
9x3 |
5x3 |
|
|
|
3x5 |
1x5 |
|
27 u |
15 u |
5 u |
37 cm2 |
Part J is the repeated identity.
LCM of 5 and 3 = 15
Part H : Part J : Part K = 27 : 15 : 5
(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 + 15 u = 5 u + 37
27 u + 15 u - 5 u = 37
37 u = 37
1 u = 37 ÷ 37 = 1
Area of the rectangle
= 2 x (5 u + 37)
= 2 x (5 x 1 + 37)
= 2 x (5 + 37)
= 2 x 42
= 84 cm
2 Answer(s): (a) 27 : 15 : 5; (b) 84 cm
2