The rectangle is divided into four parts J, K, L and M. The ratio of Part J to Part K is 7 : 2 and the ratio of Part K to Part L is 3 : 2.
- Find the ratio of Part J to Part K to Part L.
- Given that Part M is 69 cm2 , find the area of the rectangle.
(a)
J |
K |
L |
M |
7x3 |
2x3 |
|
|
|
3x2 |
2x2 |
|
21 u |
6 u |
4 u |
69 cm2 |
Part K is the repeated identity.
LCM of 2 and 3 = 6
Part J : Part K : Part L = 21 : 6 : 4
(b)
Part J + Part K = Half of the rectangle
Part L + Part M = Half of the rectangle
Part J + Part K and Part L + Part M are equal.
Part J + Part K = Part L + Part M
21 u + 6 u = 4 u + 69
21 u + 6 u - 4 u = 69
23 u = 69
1 u = 69 ÷ 23 = 3
Area of the rectangle
= 2 x (4 u + 69)
= 2 x (4 x 3 + 69)
= 2 x (12 + 69)
= 2 x 81
= 162 cm
2 Answer(s): (a) 21 : 6 : 4; (b) 162 cm
2