The figure, not drawn to scale, shows a rectangle, MNPQ, which is divided in 4 parts, R, S, T, and U. The ratio of the area of U to the area of T is 2 : 5. The ratio of the area of T to the area of S is 6 : 7. If the area of R is 408 cm
2, what is the area of the rectangle MNPQ?
U |
T |
S |
R |
2x6 |
5x6 |
|
|
|
6x5 |
7x5 |
|
12 u |
30 u |
35 u |
17 u |
Area T is the repeated identity.
LCM of 5 and 6 = 30
Half of the area of the rectangle
= Area U + Area S
= 12 u + 35 u
= 47 u
Area of R
= Half of the area of the rectangle - Area T
= 47 u - 30 u
= 17 u
17 u = 408
1 u = 408 ÷ 17 = 24
Area of the rectangle
= 47 u x 2
= 94 u
= 94 x 24
= 2256 cm
2 Answer(s): 2256 cm
2