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 2 : 5. The ratio of the area of P to the area of N is 6 : 7. If the area of M is 323 cm
2, what is the area of the rectangle HJKL?
Q |
P |
N |
M |
2x6 |
5x6 |
|
|
|
6x5 |
7x5 |
|
12 u |
30 u |
35 u |
17 u |
Area P is the repeated identity.
LCM of 5 and 6 = 30
Half of the area of the rectangle
= Area Q + Area N
= 12 u + 35 u
= 47 u
Area of M
= Half of the area of the rectangle - Area P
= 47 u - 30 u
= 17 u
17 u = 323
1 u = 323 ÷ 17 = 19
Area of the rectangle
= 47 u x 2
= 94 u
= 94 x 19
= 1786 cm
2 Answer(s): 1786 cm
2