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 1 : 2. The ratio of the area of N to the area of M is 7 : 8. If the area of L is 180 cm
2, what is the area of the rectangle GHJK?
P |
N |
M |
L |
1x7 |
2x7 |
|
|
|
7x2 |
8x2 |
|
7 u |
14 u |
16 u |
9 u |
Area N is the repeated identity.
LCM of 2 and 7 = 14
Half of the area of the rectangle
= Area P + Area M
= 7 u + 16 u
= 23 u
Area of L
= Half of the area of the rectangle - Area N
= 23 u - 14 u
= 9 u
9 u = 180
1 u = 180 ÷ 9 = 20
Area of the rectangle
= 23 u x 2
= 46 u
= 46 x 20
= 920 cm
2 Answer(s): 920 cm
2