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 7 : 9. If the area of L is 377 cm
2, what is the area of the rectangle GHJK?
P |
N |
M |
L |
1x7 |
3x7 |
|
|
|
7x3 |
9x3 |
|
7 u |
21 u |
27 u |
13 u |
Area N is the repeated identity.
LCM of 3 and 7 = 21
Half of the area of the rectangle
= Area P + Area M
= 7 u + 27 u
= 34 u
Area of L
= Half of the area of the rectangle - Area N
= 34 u - 21 u
= 13 u
13 u = 377
1 u = 377 ÷ 13 = 29
Area of the rectangle
= 34 u x 2
= 68 u
= 68 x 29
= 1972 cm
2 Answer(s): 1972 cm
2