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 5 : 7. If the area of L is 198 cm
2, what is the area of the rectangle GHJK?
P |
N |
M |
L |
1x5 |
3x5 |
|
|
|
5x3 |
7x3 |
|
5 u |
15 u |
21 u |
11 u |
Area N is the repeated identity.
LCM of 3 and 5 = 15
Half of the area of the rectangle
= Area P + Area M
= 5 u + 21 u
= 26 u
Area of L
= Half of the area of the rectangle - Area N
= 26 u - 15 u
= 11 u
11 u = 198
1 u = 198 ÷ 11 = 18
Area of the rectangle
= 26 u x 2
= 52 u
= 52 x 18
= 936 cm
2 Answer(s): 936 cm
2