The figure, not drawn to scale, shows a rectangle, STUV, which is divided in 4 parts, W, X, Y, and Z. The ratio of the area of Z to the area of Y is 1 : 3. The ratio of the area of Y to the area of X is 7 : 9. If the area of W is 195 cm
2, what is the area of the rectangle STUV?
Z |
Y |
X |
W |
1x7 |
3x7 |
|
|
|
7x3 |
9x3 |
|
7 u |
21 u |
27 u |
13 u |
Area Y is the repeated identity.
LCM of 3 and 7 = 21
Half of the area of the rectangle
= Area Z + Area X
= 7 u + 27 u
= 34 u
Area of W
= Half of the area of the rectangle - Area Y
= 34 u - 21 u
= 13 u
13 u = 195
1 u = 195 ÷ 13 = 15
Area of the rectangle
= 34 u x 2
= 68 u
= 68 x 15
= 1020 cm
2 Answer(s): 1020 cm
2