The figure, not drawn to scale, shows a rectangle, HJKL, which is divided in 4 parts, M, N, P, and Q. The ratio of the area of Q to the area of P is 1 : 4. The ratio of the area of P to the area of N is 6 : 7. If the area of M is 135 cm
2, what is the area of the rectangle HJKL?
Q |
P |
N |
M |
1x3 |
4x3 |
|
|
|
6x2 |
7x2 |
|
3 u |
12 u |
14 u |
5 u |
Area P is the repeated identity.
LCM of 4 and 6 = 12
Half of the area of the rectangle
= Area Q + Area N
= 3 u + 14 u
= 17 u
Area of M
= Half of the area of the rectangle - Area P
= 17 u - 12 u
= 5 u
5 u = 135
1 u = 135 ÷ 5 = 27
Area of the rectangle
= 17 u x 2
= 34 u
= 34 x 27
= 918 cm
2 Answer(s): 918 cm
2