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 : 3. The ratio of the area of N to the area of M is 4 : 5. If the area of L is 126 cm
2, what is the area of the rectangle GHJK?
P |
N |
M |
L |
1x4 |
3x4 |
|
|
|
4x3 |
5x3 |
|
4 u |
12 u |
15 u |
7 u |
Area N is the repeated identity.
LCM of 3 and 4 = 12
Half of the area of the rectangle
= Area P + Area M
= 4 u + 15 u
= 19 u
Area of L
= Half of the area of the rectangle - Area N
= 19 u - 12 u
= 7 u
7 u = 126
1 u = 126 ÷ 7 = 18
Area of the rectangle
= 19 u x 2
= 38 u
= 38 x 18
= 684 cm
2 Answer(s): 684 cm
2