I have a question in my homework.

Question

Azhar is given a piece of wire of length Lcm to be bent into the shape of a rectangle with an area of 10.24cm2 . Find the shortest wire,l in order to achieve given task

Answer 1

Let x is length and y is width of wire,Then we have: xy = 10.24; y = 10.24/x;

L = 2x + 2y = 2x + 20.48/x; dL/dx = 2 - 20.48/x² = 0; x² = 10.24; x = 3.2 cm

L'' = 40.96/x³; L''(3.2 ) = 40.96/3.2³ =1.25 > 0. So we have minimum

L_min = 2·3.2 + 20.48/3.2 = 12.8 cm