Problems Involving Maximisation and Minimisation Q1

The perimeter of an isosceles triangle of base length \(x\) cm and two sides of equal length \(y\) cm is \(10\) cm.

By using differentiation, show that when the area of the triangle is maximum,

1. the triangle is equilateral,
2. the area is \(\frac{25\sqrt{3}}{9}\) units².