The figure, not drawn to scale, shows a rectangle, QRST, which is divided in 4 parts, U, V, W, and X. The ratio of the area of X to the area of W is 2 : 7. The ratio of the area of W to the area of V is 9 : 10. If the area of U is 725 cm
2, what is the area of the rectangle QRST?
X |
W |
V |
U |
2x9 |
7x9 |
|
|
|
9x7 |
10x7 |
|
18 u |
63 u |
70 u |
25 u |
Area W is the repeated identity.
LCM of 7 and 9 = 63
Half of the area of the rectangle
= Area X + Area V
= 18 u + 70 u
= 88 u
Area of U
= Half of the area of the rectangle - Area W
= 88 u - 63 u
= 25 u
25 u = 725
1 u = 725 ÷ 25 = 29
Area of the rectangle
= 88 u x 2
= 176 u
= 176 x 29
= 5104 cm
2 Answer(s): 5104 cm
2