Question

A friend gives you a puppy for your birthday and offers to buy fencing for a dog run. What shape gives your puppy more area to run: a rectangle whose width is twice the length, a regular hexagon, or a square?

Answer 1

Regular hexagon will give puppy more area to run.

Explanation:

We are given the following in the question:

Shapes: rectangle, regular hexagon, square

Rectangle:

Length,l = a

Width, w = 2a

Area of rectangle =

`A = l* w\\A = a* 2a=2a^2`

Regular hexagon:

Side length,s = a

Area of hexagon =

`A =(3√(3))/(2)a^2`

Square:

Side length, s = a

Area of square =

`A = a^2`

Comparison:

`a^2<2a^2<(3√(3))/(2)a^2`

Thus, regular hexagon will give puppy more area to run.