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 1 : 3. The ratio of the area of W to the area of V is 7 : 8. If the area of U is 290 cm
2, what is the area of the rectangle QRST?
X |
W |
V |
U |
1x7 |
3x7 |
|
|
|
7x3 |
8x3 |
|
7 u |
21 u |
24 u |
10 u |
Area W is the repeated identity.
LCM of 3 and 7 = 21
Half of the area of the rectangle
= Area X + Area V
= 7 u + 24 u
= 31 u
Area of U
= Half of the area of the rectangle - Area W
= 31 u - 21 u
= 10 u
10 u = 290
1 u = 290 ÷ 10 = 29
Area of the rectangle
= 31 u x 2
= 62 u
= 62 x 29
= 1798 cm
2 Answer(s): 1798 cm
2