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 : 5. The ratio of the area of X to the area of W is 8 : 9. If the area of V is 567 cm
2, what is the area of the rectangle RSTU?
Y |
X |
W |
V |
2x8 |
5x8 |
|
|
|
8x5 |
9x5 |
|
16 u |
40 u |
45 u |
21 u |
Area X is the repeated identity.
LCM of 5 and 8 = 40
Half of the area of the rectangle
= Area Y + Area W
= 16 u + 45 u
= 61 u
Area of V
= Half of the area of the rectangle - Area X
= 61 u - 40 u
= 21 u
21 u = 567
1 u = 567 ÷ 21 = 27
Area of the rectangle
= 61 u x 2
= 122 u
= 122 x 27
= 3294 cm
2 Answer(s): 3294 cm
2