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 : 4. The ratio of the area of V to the area of U is 9 : 10. If the area of T is 312 cm
2, what is the area of the rectangle PQRS?
W |
V |
U |
T |
1x9 |
4x9 |
|
|
|
9x4 |
10x4 |
|
9 u |
36 u |
40 u |
13 u |
Area V is the repeated identity.
LCM of 4 and 9 = 36
Half of the area of the rectangle
= Area W + Area U
= 9 u + 40 u
= 49 u
Area of T
= Half of the area of the rectangle - Area V
= 49 u - 36 u
= 13 u
13 u = 312
1 u = 312 ÷ 13 = 24
Area of the rectangle
= 49 u x 2
= 98 u
= 98 x 24
= 2352 cm
2 Answer(s): 2352 cm
2