construct an isoceles triangle with an area of 100. what is the length of the base of the triangle which has the smallest perimeter?
Prepping for a test, explanations please
let L = length of equal legs
let x = base lenth
let altitude = h
then h^2 + (x/2)^2 = L^2
h = sqrt(L^2 - .25 x^2)
area = 100 = (1/2)xh
= (1/2)x sqrt(L^2-.25x^2)
perimeter = 2L + x
d perimeter/dx = 0 = 2 dL/dx + 1 for min or max
so when dL/dx = -1/2
but
d/dx 100 = 0 so
0 = x d/dx (L^2-.25x^2)^.5 + (L^2-.25 x^2)^.5
solve for L/x