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 : 7. If the area of V is 252 cm
2, what is the area of the rectangle RSTU?
Y |
X |
W |
V |
1x5 |
2x5 |
|
|
|
5x2 |
7x2 |
|
5 u |
10 u |
14 u |
9 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 + 14 u
= 19 u
Area of V
= Half of the area of the rectangle - Area X
= 19 u - 10 u
= 9 u
9 u = 252
1 u = 252 ÷ 9 = 28
Area of the rectangle
= 19 u x 2
= 38 u
= 38 x 28
= 1064 cm
2 Answer(s): 1064 cm
2