The perimeter of an isosceles triangle of base length $x$ cm and two sides of equal length $y$ cm ea

Question

The perimeter of an isosceles triangle of base length $x$ cm and two sides of equal length $y$ cm each is $12$ cm. Show that its area can be expressed as $\frac{x}{2}\sqrt{36-6x}$. Hence show that the area is maximum when the triangle is equilateral.

Accepted Answer

$A=\frac x2\sqrt{36-6x}$ Maximum when $x=y=4\text{ cm}$, so the triangle is equilateral

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