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 2 : 5. The ratio of the area of V to the area of U is 4 : 5. If the area of T is 169 cm
2, what is the area of the rectangle PQRS?
| W |
V |
U |
T |
| 2x4 |
5x4 |
|
|
| |
4x5 |
5x5 |
|
| 8 u |
20 u |
25 u |
13 u |
Area V is the repeated identity.
LCM of 5 and 4 = 20
Half of the area of the rectangle
= Area W + Area U
= 8 u + 25 u
= 33 u
Area of T
= Half of the area of the rectangle - Area V
= 33 u - 20 u
= 13 u
13 u = 169
1 u = 169 ÷ 13 = 13
Area of the rectangle
= 33 u x 2
= 66 u
= 66 x 13
= 858 cm
2 Answer(s): 858 cm
2 
