Probem23+James,+Marnie

Very good!!

Problem 23:

Optimization Equation: A = x over (L,0)

Lim A = 0 x→ L

Lim A = 0 x→ 0 L is a constant

A‘ = L(√3 / 2) - x√3 0 = L(√3 / 2) - x√3 x√3 = L(√3 / 2) x=L/2

Plug L/2 back into the first part of the original function. = ((L-L/2)√3) / 2 = ((L/2)√3) / 2 = (L√3)/4 Therefore the dimensions of the largest possible rectangle inscribed in an equilateral triangle of side length L would be (L/2), (L√3)/4