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 : 2. The ratio of the area of V to the area of U is 7 : 8. If the area of T is 225 cm
2, what is the area of the rectangle PQRS?
| W |
V |
U |
T |
| 1x7 |
2x7 |
|
|
| |
7x2 |
8x2 |
|
| 7 u |
14 u |
16 u |
9 u |
Area V is the repeated identity.
LCM of 2 and 7 = 14
Half of the area of the rectangle
= Area W + Area U
= 7 u + 16 u
= 23 u
Area of T
= Half of the area of the rectangle - Area V
= 23 u - 14 u
= 9 u
9 u = 225
1 u = 225 ÷ 9 = 25
Area of the rectangle
= 23 u x 2
= 46 u
= 46 x 25
= 1150 cm
2 Answer(s): 1150 cm
2 
