The figure, not drawn to scale, shows a rectangle, FGHJ, which is divided in 4 parts, K, L, M, and N. The ratio of the area of N to the area of M is 1 : 4. The ratio of the area of M to the area of L is 7 : 9. If the area of K is 375 cm
2, what is the area of the rectangle FGHJ?
N |
M |
L |
K |
1x7 |
4x7 |
|
|
|
7x4 |
9x4 |
|
7 u |
28 u |
36 u |
15 u |
Area M is the repeated identity.
LCM of 4 and 7 = 28
Half of the area of the rectangle
= Area N + Area L
= 7 u + 36 u
= 43 u
Area of K
= Half of the area of the rectangle - Area M
= 43 u - 28 u
= 15 u
15 u = 375
1 u = 375 ÷ 15 = 25
Area of the rectangle
= 43 u x 2
= 86 u
= 86 x 25
= 2150 cm
2 Answer(s): 2150 cm
2