Problems with perimeter

Question

A quadrilateral has an area of 100 cm2 . What is the minimum perimeter this shape could have? Explain your reasoning.

Answer 1

40 cm = minimum perimeter if area = 100 cm

a square has minimum perimeter for a fixed area

or use calculus

A= Lw = 100

L=100/w

P = 2L+2w = 200/w + 2w

P'(w) = 2 -200/w^2 = 0

2w^2 =200

w^2 = 100

w = 10

L = 100/10 = 10

P=2L+2w = 2(10)+2(10)= 40 cm