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 5 : 6. If the area of V is 98 cm
2, what is the area of the rectangle RSTU?
Y |
X |
W |
V |
1x5 |
2x5 |
|
|
|
5x2 |
6x2 |
|
5 u |
10 u |
12 u |
7 u |
Area X is the repeated identity.
LCM of 2 and 5 = 10
Half of the area of the rectangle
= Area Y + Area W
= 5 u + 12 u
= 17 u
Area of V
= Half of the area of the rectangle - Area X
= 17 u - 10 u
= 7 u
7 u = 98
1 u = 98 ÷ 7 = 14
Area of the rectangle
= 17 u x 2
= 34 u
= 34 x 14
= 476 cm
2 Answer(s): 476 cm
2