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

Answer:

Regular hexagon will give puppy more area to run.

Step-by-step explanation:

We are given the following in the question:

Shapes: rectangle, regular hexagon, square

Rectangle:

Length,l = a

Width, w = 2a

Area of rectangle =

$A = l\times w\\A = a\times 2a=2a^2$

Regular hexagon:

Side length,s = a

Area of hexagon =

$A =\dfrac{3\sqrt{3}}{2}a^2$

Square:

Side length, s = a

Area of square =

$A = a^2$

Comparison:

$a^2<2a^2<\dfrac{3\sqrt{3}}{2}a^2$

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