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 : 7. The ratio of the area of P to the area of N is 8 : 9. If the area of M is 575 cm
2, what is the area of the rectangle HJKL?
Q |
P |
N |
M |
2x8 |
7x8 |
|
|
|
8x7 |
9x7 |
|
16 u |
56 u |
63 u |
23 u |
Area P is the repeated identity.
LCM of 7 and 8 = 56
Half of the area of the rectangle
= Area Q + Area N
= 16 u + 63 u
= 79 u
Area of M
= Half of the area of the rectangle - Area P
= 79 u - 56 u
= 23 u
23 u = 575
1 u = 575 ÷ 23 = 25
Area of the rectangle
= 79 u x 2
= 158 u
= 158 x 25
= 3950 cm
2 Answer(s): 3950 cm
2