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 1 : 2. The ratio of the area of X to the area of W is 7 : 9. If the area of V is 198 cm
2, what is the area of the rectangle RSTU?
Y |
X |
W |
V |
1x7 |
2x7 |
|
|
|
7x2 |
9x2 |
|
7 u |
14 u |
18 u |
11 u |
Area X is the repeated identity.
LCM of 2 and 7 = 14
Half of the area of the rectangle
= Area Y + Area W
= 7 u + 18 u
= 25 u
Area of V
= Half of the area of the rectangle - Area X
= 25 u - 14 u
= 11 u
11 u = 198
1 u = 198 ÷ 11 = 18
Area of the rectangle
= 25 u x 2
= 50 u
= 50 x 18
= 900 cm
2 Answer(s): 900 cm
2