The figure, not drawn to scale, shows a rectangle, EFGH, which is divided in 4 parts, J, K, L, and M. The ratio of the area of M to the area of L is 1 : 3. The ratio of the area of L to the area of K is 7 : 8. If the area of J is 190 cm
2, what is the area of the rectangle EFGH?
M |
L |
K |
J |
1x7 |
3x7 |
|
|
|
7x3 |
8x3 |
|
7 u |
21 u |
24 u |
10 u |
Area L is the repeated identity.
LCM of 3 and 7 = 21
Half of the area of the rectangle
= Area M + Area K
= 7 u + 24 u
= 31 u
Area of J
= Half of the area of the rectangle - Area L
= 31 u - 21 u
= 10 u
10 u = 190
1 u = 190 ÷ 10 = 19
Area of the rectangle
= 31 u x 2
= 62 u
= 62 x 19
= 1178 cm
2 Answer(s): 1178 cm
2