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 9 : 10. If the area of M is 750 cm
2, what is the area of the rectangle HJKL?
Q |
P |
N |
M |
2x9 |
7x9 |
|
|
|
9x7 |
10x7 |
|
18 u |
63 u |
70 u |
25 u |
Area P is the repeated identity.
LCM of 7 and 9 = 63
Half of the area of the rectangle
= Area Q + Area N
= 18 u + 70 u
= 88 u
Area of M
= Half of the area of the rectangle - Area P
= 88 u - 63 u
= 25 u
25 u = 750
1 u = 750 ÷ 25 = 30
Area of the rectangle
= 88 u x 2
= 176 u
= 176 x 30
= 5280 cm
2 Answer(s): 5280 cm
2