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 : 4. The ratio of the area of W to the area of V is 7 : 9. If the area of U is 345 cm
2, what is the area of the rectangle QRST?
X |
W |
V |
U |
1x7 |
4x7 |
|
|
|
7x4 |
9x4 |
|
7 u |
28 u |
36 u |
15 u |
Area W is the repeated identity.
LCM of 4 and 7 = 28
Half of the area of the rectangle
= Area X + Area V
= 7 u + 36 u
= 43 u
Area of U
= Half of the area of the rectangle - Area W
= 43 u - 28 u
= 15 u
15 u = 345
1 u = 345 ÷ 15 = 23
Area of the rectangle
= 43 u x 2
= 86 u
= 86 x 23
= 1978 cm
2 Answer(s): 1978 cm
2