The figure, not drawn to scale, shows a rectangle, GHJK, which is divided in 4 parts, L, M, N, and P. The ratio of the area of P to the area of N is 2 : 5. The ratio of the area of N to the area of M is 7 : 9. If the area of L is 360 cm
2, what is the area of the rectangle GHJK?
P |
N |
M |
L |
2x7 |
5x7 |
|
|
|
7x5 |
9x5 |
|
14 u |
35 u |
45 u |
24 u |
Area N is the repeated identity.
LCM of 5 and 7 = 35
Half of the area of the rectangle
= Area P + Area M
= 14 u + 45 u
= 59 u
Area of L
= Half of the area of the rectangle - Area N
= 59 u - 35 u
= 24 u
24 u = 360
1 u = 360 ÷ 24 = 15
Area of the rectangle
= 59 u x 2
= 118 u
= 118 x 15
= 1770 cm
2 Answer(s): 1770 cm
2