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:



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:



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:



Finally, since all sides in the hexagon have the same length, we can see that side UV must have length 2


At this point, we can see that x = 1 + 2 + 1 = 4
And y = √3 + √3 = 2√3

We 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 1

Answer: A

Cheers,
Brent
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Why?

why stands for an explanation ?'

why means zero...........

I don’t understand how to arrive at the solution.

Posted from my mobile device

This will go on Instagram. I take a lottttttttt of shortcuts.

However, your explanation is amazing.

very detailed

Thanks

Thanks Carcass!!
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as it is given in the question that polygon is equilateral and equiangular, which means all sides of polygon are equal and all internal angles (also external) are equal.
sum of interior angle of any polygon can be found by using formula (n-2)x180, where 'n' is the number of sides of polygon.
if all sides are equal and equiangular then divide the above formula by 'n' to find the value of one interior angle.
after calculating interior angle, find the exterior angle by subtracting interior angle from 180. which gives 30-60-90 triangle then calculate 'x' and 'y', which shows that x>y. therefore x/y is greater than 1.
answer is A.

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

That's correct.
I choose 1: root 3: 2, since they're easy to work with.

Using 2: 2 root 3 : 4 will also yield the correct answer.
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Quick answer:

Polygon given is a regular hexagon.

Relevant principle: You can 'cut' a regular hexagon into 6 equal EQUILATERAL triangles: three on the top and three on the bottom.

If a is the length of each side of the six equilateral triangles, then length of the rectangle, x happens to be 2a and the width stands as \(2*\sqrt{3}/2*a\).

\(x/y\) then simplifies as \(\frac{2}{\sqrt{3}}\), which is greater then 1.

Hence A is the answer.