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 : 7. The ratio of the area of X to the area of W is 4 : 5. If the area of V is 180 cm
2, what is the area of the rectangle RSTU?
Y |
X |
W |
V |
2x4 |
7x4 |
|
|
|
4x7 |
5x7 |
|
8 u |
28 u |
35 u |
15 u |
Area X is the repeated identity.
LCM of 7 and 4 = 28
Half of the area of the rectangle
= Area Y + Area W
= 8 u + 35 u
= 43 u
Area of V
= Half of the area of the rectangle - Area X
= 43 u - 28 u
= 15 u
15 u = 180
1 u = 180 ÷ 15 = 12
Area of the rectangle
= 43 u x 2
= 86 u
= 86 x 12
= 1032 cm
2 Answer(s): 1032 cm
2