The figure, not drawn to scale, shows a rectangle, RSTU, which is divided in 4 parts, V, W, X, and Y. The ratio of the area of Y to the area of X is 2 : 7. The ratio of the area of X to the area of W is 8 : 9. If the area of V is 644 cm
2, what is the area of the rectangle RSTU?
| Y |
X |
W |
V |
| 2x8 |
7x8 |
|
|
| |
8x7 |
9x7 |
|
| 16 u |
56 u |
63 u |
23 u |
Area X is the repeated identity.
LCM of 7 and 8 = 56
Half of the area of the rectangle
= Area Y + Area W
= 16 u + 63 u
= 79 u
Area of V
= Half of the area of the rectangle - Area X
= 79 u - 56 u
= 23 u
23 u = 644
1 u = 644 ÷ 23 = 28
Area of the rectangle
= 79 u x 2
= 158 u
= 158 x 28
= 4424 cm
2 Answer(s): 4424 cm
2 
