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 1 : 3. The ratio of the area of T to the area of S is 5 : 6. If the area of R is 200 cm
2, what is the area of the rectangle MNPQ?
U |
T |
S |
R |
1x5 |
3x5 |
|
|
|
5x3 |
6x3 |
|
5 u |
15 u |
18 u |
8 u |
Area T is the repeated identity.
LCM of 3 and 5 = 15
Half of the area of the rectangle
= Area U + Area S
= 5 u + 18 u
= 23 u
Area of R
= Half of the area of the rectangle - Area T
= 23 u - 15 u
= 8 u
8 u = 200
1 u = 200 ÷ 8 = 25
Area of the rectangle
= 23 u x 2
= 46 u
= 46 x 25
= 1150 cm
2 Answer(s): 1150 cm
2