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 9 : 10. If the area of L is 108 cm
2, what is the area of the rectangle GHJK?
P |
N |
M |
L |
1x3 |
3x3 |
|
|
|
9x1 |
10x1 |
|
3 u |
9 u |
10 u |
4 u |
Area N is the repeated identity.
LCM of 3 and 9 = 9
Half of the area of the rectangle
= Area P + Area M
= 3 u + 10 u
= 13 u
Area of L
= Half of the area of the rectangle - Area N
= 13 u - 9 u
= 4 u
4 u = 108
1 u = 108 ÷ 4 = 27
Area of the rectangle
= 13 u x 2
= 26 u
= 26 x 27
= 702 cm
2 Answer(s): 702 cm
2