Question

A 180 foot length of fence is placed around a three-sided animal pen. Two of the sides of the pen are 72 feet and 78 feet. Does the fence form a right triangle?

Answer 1

Answer:

Yes

Step-by-step explanation:

Length of the third side

$180-(72+78)=30\ \text{ft}$

The hypotenuse is always the longest side of a right triangle.

So, the hypotenuse here is $c=78\ \text{ft}$

$a=72\ \text{ft},b=30\ \text{ft}$

$c=\sqrt{a^2+b^2}\\\Rightarrow c=\sqrt{72^2+30^2}\\\Rightarrow c=\sqrt{6084}\\\Rightarrow c=78\ \text{ft}$

The Pythagoras theorem applies so the fence does form a right triangle.