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 8 : 9. If the area of T is 273 cm
2, what is the area of the rectangle PQRS?
W |
V |
U |
T |
2x8 |
5x8 |
|
|
|
8x5 |
9x5 |
|
16 u |
40 u |
45 u |
21 u |
Area V is the repeated identity.
LCM of 5 and 8 = 40
Half of the area of the rectangle
= Area W + Area U
= 16 u + 45 u
= 61 u
Area of T
= Half of the area of the rectangle - Area V
= 61 u - 40 u
= 21 u
21 u = 273
1 u = 273 ÷ 21 = 13
Area of the rectangle
= 61 u x 2
= 122 u
= 122 x 13
= 1586 cm
2 Answer(s): 1586 cm
2