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 9 : 10. If the area of W is 68 cm
2, what is the area of the rectangle STUV?
Z |
Y |
X |
W |
1x3 |
3x3 |
|
|
|
9x1 |
10x1 |
|
3 u |
9 u |
10 u |
4 u |
Area Y is the repeated identity.
LCM of 3 and 9 = 9
Half of the area of the rectangle
= Area Z + Area X
= 3 u + 10 u
= 13 u
Area of W
= Half of the area of the rectangle - Area Y
= 13 u - 9 u
= 4 u
4 u = 68
1 u = 68 ÷ 4 = 17
Area of the rectangle
= 13 u x 2
= 26 u
= 26 x 17
= 442 cm
2 Answer(s): 442 cm
2