Question

You have 200 meters of fencing. What triangle will result in the maximum fence-able area? What is that area?

Answer 1

Answer:

It will be an equilateral triangle and the area is 1924.5 sq. meters.

Step-by-step explanation:

If the total length of the fencing of 200 meters is utilized then the perimeter of the triangle will be 200 meters.

Now, we know that the type of triangle that gives the maximum area for a given perimeter is an equilateral triangle.

So, the equilateral triangle with a perimeter of 200 meters will have side lengths of $\frac{200}{3}$ meters.

Now, the area of an equilateral triangle with sides a units is given by $\frac{\sqrt{3}}{4} a^{2}$ sq. units.

So, the area of the above equilateral triangle will be = $\frac{\sqrt{3}}{4}\times (\frac{200}{3})^{2} = 1924.5$ sq. meters. (Answer)