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 2 : 7. The ratio of the area of Y to the area of X is 9 : 10. If the area of W is 475 cm
2, what is the area of the rectangle STUV?
Z |
Y |
X |
W |
2x9 |
7x9 |
|
|
|
9x7 |
10x7 |
|
18 u |
63 u |
70 u |
25 u |
Area Y is the repeated identity.
LCM of 7 and 9 = 63
Half of the area of the rectangle
= Area Z + Area X
= 18 u + 70 u
= 88 u
Area of W
= Half of the area of the rectangle - Area Y
= 88 u - 63 u
= 25 u
25 u = 475
1 u = 475 ÷ 25 = 19
Area of the rectangle
= 88 u x 2
= 176 u
= 176 x 19
= 3344 cm
2 Answer(s): 3344 cm
2