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Yes.

Heron's formula for the area of a triangle is A = √[s(s-a)(s-b)(s-c)] where a,b,c are the lengths of the sides of a triangle and s = 1/2(a+b+c). When a+b+c = 200 then s = 100.

The sum of the lengths of two sides of a triangle must always exceed the length of the remaining side. The maximum area is when all three sides are of equal length, therefore the side length is 662/3 and s-a = s-b = s-c = 100 - 662/3 = 331/3.

A = √[100 x (331/3)3] = 1924 sq units.

The minimum area is provided by a long, narrow triangle. If an isosceles triangle is taken with the base length of 24 units and each equal side measuring 88 units then this triangle has a perimeter of 200 and an area of 1046 sq units. Provided the base length is not shortened then as the triangle 'widens' the area increases.

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Q: Can the perimeter of a triangle be 200 when the area is in the 1000?
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