Twenty metres of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of the circle in meters be, if we wish to have a flower bed with the greatest possible surface area?

So, we know that that:

r+r+arc = 20
2r+arc=20

To find an arc length we multiply the circumference by (x/360) where x is the measure of the central angle.
Arc Measurement = (x/360) * pi*D

The problem is, we don't know what the central angle is.

Using formula: 2r + (q/2pi)*(pi*d) = 20
(I am familiar with finding the arc measurement/area with (x/360) Where is (q/2Pi) coming from? Is this for when we don't know what the central angle is?

From that point on, I am lost, specifically regarding "maximizing" the value.

(1) 2√2
(2) 2√5
(3) 5
(4) 4√2
(5) none of these

You don't need derivatives in CAT either! Anyway, we can solve it either by plugging in numbers or by using this concept:
If the sum of given numbers is constant, their product is maximum when they are equal.

Given: \(2r + (\frac{Q}{2pi})*2*pi*r = 20\)
i.e. \(2r + Qr = 20\)

Maximize \((\frac{Q}{2pi})*pi*r^2 = \frac{Qr^2}{2}\)
Now \(Qr = 20 - 2r\) from above. So, Maximize \((20-2r)r/2 = (10 - r)r\)
Since \(10 - r + r = 10\), to maximize product, \(10 - r = r\) i.e. \(r = 5\)

As the original poster said, this is not a GMAT question. GMAT questions do not have 'None of the above' as an option. So you can test options in GMAT if the question permits.

\(2*\pi\) radians = 360 degrees (just like 1 km = 1000 m) (Recall that \(\pi = 3.1416\) approx)
So about 6.28 radians = 360 degrees

As for our question:
Qr = 20 - 2r (where Q is in radians since we used \(Q/2\pi\) in the formula)
Put r = 5 here, you get Q = 2 radians (not degrees)

2 radians = \(360/\pi\) degrees = 114.6 degrees

Also why would you assume that it must be equilateral? What is the logic behind that? It is a sector we are talking about, not a triangle.

A for me .Hello guys, I don't know whether my answer is correct. For a sector to have greater area and circumference,sector should have greater central angle.In options given A gives higher (305).

I know a concept that for a given perimeter equilateral triangle gives maximum area, so this sector must be similar to an equilateral triangle with sides 20/3 = 6.66, it means radius should be less than 6, in answer choices 5 is given so it is the nearest possible sector, other choices are not even around 6.