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 7 : 9. If the area of T is 432 cm
2, what is the area of the rectangle PQRS?
W |
V |
U |
T |
2x7 |
5x7 |
|
|
|
7x5 |
9x5 |
|
14 u |
35 u |
45 u |
24 u |
Area V is the repeated identity.
LCM of 5 and 7 = 35
Half of the area of the rectangle
= Area W + Area U
= 14 u + 45 u
= 59 u
Area of T
= Half of the area of the rectangle - Area V
= 59 u - 35 u
= 24 u
24 u = 432
1 u = 432 ÷ 24 = 18
Area of the rectangle
= 59 u x 2
= 118 u
= 118 x 18
= 2124 cm
2 Answer(s): 2124 cm
2