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 4 : 5. If the area of V is 234 cm
2, what is the area of the rectangle RSTU?
Y |
X |
W |
V |
2x4 |
5x4 |
|
|
|
4x5 |
5x5 |
|
8 u |
20 u |
25 u |
13 u |
Area X is the repeated identity.
LCM of 5 and 4 = 20
Half of the area of the rectangle
= Area Y + Area W
= 8 u + 25 u
= 33 u
Area of V
= Half of the area of the rectangle - Area X
= 33 u - 20 u
= 13 u
13 u = 234
1 u = 234 ÷ 13 = 18
Area of the rectangle
= 33 u x 2
= 66 u
= 66 x 18
= 1188 cm
2 Answer(s): 1188 cm
2