Question

A rectangle has area 25 m2. express the perimeter of the rectangle as a function of the length l of one of its sides. p(l) = state the domain of p. (assume the length of the rectangle is larger than its width. enter your answer using interval notation.)

Answer 1

a) The area of a rectangle is the product of length and width:
   A = l·w

This formula gives us a way to represent the width in terms of area and length. Divide by l to get
   A/l = w

Now we know that the perimeter of a rectangle is the sum of the lengths of its sides.
   P = l + w + l + w
   P = 2(l + w)
We want to find a formula that just has l on the right, so we can use the expression for w from above.
   P = 2(l +A/l)

Substituting the given number for A, the function p(l) can be written as
   p(l) = 2(l +25/l)
   p(l) = 2l +50/l


b) For length greater than width, we have
   l > w
   l > A/l
   l² > A
   l > √A
   l > √25

This means the domain of p(l) is
   l ∈ (5, ∞) . . . . . meters