Question

A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. Find the maximum and minimum possible area that can be enclosed by the wire.

Answer 1

Given :

A piece of wire 10 m long is cut into two pieces.

To Find :

One piece is bent into a square and the other is bent into an equilateral triangle.

Solution :

So, perimeter of triangle is 5 m :

`6a = 5 \\\\a = (5)/(6)\ m`

Area of triangle of side a :

`Area = a^2 \\\\Area = ((5)/(6))^2\\\\Area = 0.694\ m^2`

Now. we know maximum area of a given perimeter is for equilateral triangle.

3s = 5

`s=(5)/(3)`

`Area = (\sqrt3)/(4)s^2\\\\Area = (\sqrt3)/(4)* ((5)/(3))^2\\\\Area =1.20 \ m^2`

Hence, this is the required solution.