Show that of all the isosceles triangles with a given perimeter, the one with the greatest area is equilateral.
I hardly even know where to start...
2006-10-13 08:59:08 · 2 answers · asked by adriana_00000 2 in Education & Reference ➔ Homework Help
This is a maximization problem. You know how to calculate the area of isosceles triangles. Take the formula and think of it as a graph with two variables (base and height), and result being area.
Use what you know of calculus to maximize. Try to show that for the triangle, if all sides are equal, maximum area is obtained.
2006-10-13 09:22:59 · answer #1 · answered by freddrick_flintstone 3 · 0⤊ 0⤋
the question can truly be solved by technique of factorization or H'lopital's rule. by technique of factorization we've lim x->3 (x-3)(x+3)/(x-3)(x^2+3x+9). then you actually opt to cancel the bracket (x-3) both in the numerator and the denominator that were making the function to be of the indeterminate variety 0/0. Then ultimately be conscious the obstacles by technique of substituting x=3 in the re-defined function i.e lim x->3 (x+3)/(x^2+3x+9) to get 6/27 because the reduce.
2016-12-04 19:20:42 · answer #2 · answered by ? 4 · 0⤊ 0⤋