Jerry plans to fence a rectangular area with 100m of fencing. what is the maximum possible area that he can enclose with this fencing? (word problems on quadratic functions)

Area of circle = πr²

Perimeter (circumference) = 2πr

∴ πr² = 4(2πr)

→ πr² = 8πr

→ r = 8 units.

Here, r is the radius. Radius is 8 units.

Here, there is a very interesting fact. The largest possible triangle that can be inscribed on a circle is an equilateral triangle.

It has an area of a√b.

Now, there is a very interesting formula:

Area of equilateral triangle inscribed in a circle:

3/4 × r² × √3

r = 8.

→ 3/4 × 8² × √3

→ 48√3.

Another formula, A = √3 /4 × a²

Therefore,

48√3 = √3 /4 × a²

48 × 4 = a²

a = √192

a = 8√3

Then, b = (1/2) * √3 * a

b = (1/2) * √3 * 8√3

b = 12.

a+b = 8√3 + 12.

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