The ratio will be 1: root 3: 2, but that's the value of the sides right? It could also be 2: 2 root 3 : 4
Carcass wrote:
Attachment:
#GREpracticequestion Polygon SUVNPQ is equilateral and equiangular and TWOR is a rectangle.jpg
Polygon SUVNPQ is equilateral and equiangular and TWOR is a rectangle.
Quantity A |
Quantity B |
\(\frac{x}{y}\) |
\(1\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
I'm not sure why the test-makers didn't just say that
SUVNPQ is a regular hexagon.
Anyhoo....we know that
the sum of the angles in an n-sided polygon = (n - 2)(180°)So, in a 6-sided hexagon, the sum of the angles = (6 - 2)(180°) = 720°
Since there are 6 angles, each angle = 720°/6 =
120°So, let's add this to the diagram:
Attachment:
Polygon SUVNPQ is equilateral-1.png
Since angles on a line add to 180° and since angles in a triangle must add to 180°, we can add the following angles to the diagram:
Attachment:
Polygon SUVNPQ is equilateral-2.png
At this point, we can see we have 4 special 30-60-90 right triangles hiding in our diagram. So, let's let each side have the same measurements as our BASE 30-60-90 right triangle:
Attachment:
Polygon SUVNPQ is equilateral-3.png
Finally, since all sides in the hexagon have the same length, we can see that side UV must have length 2
Attachment:
Polygon SUVNPQ is equilateral-4.png
At this point, we can see that x =
1 +
2 +
1 =
4And y =
√3 +
√3 =
2√3We get:
Quantity A: x/y =
4/
2√3 = 2/√3
Quantity B: 1
Since √3 ≈ 1.7, we know that
2/√3 is greater than 1Answer: A
Cheers,
Brent