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 : 3. The ratio of the area of P to the area of N is 7 : 8. If the area of M is 280 cm
2, what is the area of the rectangle HJKL?
Q |
P |
N |
M |
1x7 |
3x7 |
|
|
|
7x3 |
8x3 |
|
7 u |
21 u |
24 u |
10 u |
Area P is the repeated identity.
LCM of 3 and 7 = 21
Half of the area of the rectangle
= Area Q + Area N
= 7 u + 24 u
= 31 u
Area of M
= Half of the area of the rectangle - Area P
= 31 u - 21 u
= 10 u
10 u = 280
1 u = 280 ÷ 10 = 28
Area of the rectangle
= 31 u x 2
= 62 u
= 62 x 28
= 1736 cm
2 Answer(s): 1736 cm
2