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 : 2. The ratio of the area of P to the area of N is 5 : 6. If the area of M is 189 cm
2, what is the area of the rectangle HJKL?
Q |
P |
N |
M |
1x5 |
2x5 |
|
|
|
5x2 |
6x2 |
|
5 u |
10 u |
12 u |
7 u |
Area P is the repeated identity.
LCM of 2 and 5 = 10
Half of the area of the rectangle
= Area Q + Area N
= 5 u + 12 u
= 17 u
Area of M
= Half of the area of the rectangle - Area P
= 17 u - 10 u
= 7 u
7 u = 189
1 u = 189 ÷ 7 = 27
Area of the rectangle
= 17 u x 2
= 34 u
= 34 x 27
= 918 cm
2 Answer(s): 918 cm
2