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 5 : 7. If the area of L is 126 cm
2, what is the area of the rectangle GHJK?
P |
N |
M |
L |
1x5 |
2x5 |
|
|
|
5x2 |
7x2 |
|
5 u |
10 u |
14 u |
9 u |
Area N is the repeated identity.
LCM of 2 and 5 = 10
Half of the area of the rectangle
= Area P + Area M
= 5 u + 14 u
= 19 u
Area of L
= Half of the area of the rectangle - Area N
= 19 u - 10 u
= 9 u
9 u = 126
1 u = 126 ÷ 9 = 14
Area of the rectangle
= 19 u x 2
= 38 u
= 38 x 14
= 532 cm
2 Answer(s): 532 cm
2