The figure, not drawn to scale, shows a rectangle, PQRS, which is divided in 4 parts, T, U, V, and W. The ratio of the area of W to the area of V is 1 : 3. The ratio of the area of V to the area of U is 5 : 6. If the area of T is 240 cm
2, what is the area of the rectangle PQRS?
W |
V |
U |
T |
1x5 |
3x5 |
|
|
|
5x3 |
6x3 |
|
5 u |
15 u |
18 u |
8 u |
Area V is the repeated identity.
LCM of 3 and 5 = 15
Half of the area of the rectangle
= Area W + Area U
= 5 u + 18 u
= 23 u
Area of T
= Half of the area of the rectangle - Area V
= 23 u - 15 u
= 8 u
8 u = 240
1 u = 240 ÷ 8 = 30
Area of the rectangle
= 23 u x 2
= 46 u
= 46 x 30
= 1380 cm
2 Answer(s): 1380 cm
2