Answered

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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?

Sagot :

boffeemadrid

Answer:

Yes

Step-by-step explanation:

Length of the third side

[tex]180-(72+78)=30\ \text{ft}[/tex]

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

So, the hypotenuse here is [tex]c=78\ \text{ft}[/tex]

[tex]a=72\ \text{ft},b=30\ \text{ft}[/tex]

[tex]c=\sqrt{a^2+b^2}\\\Rightarrow c=\sqrt{72^2+30^2}\\\Rightarrow c=\sqrt{6084}\\\Rightarrow c=78\ \text{ft}[/tex]

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

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