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

Yes

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=√(a^2+b^2)\\\Rightarrow c=√(72^2+30^2)\\\Rightarrow c=√(6084)\\\Rightarrow c=78\ \text{ft}`

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