Radical's and Pythagorean Theorem

[markl77]

Hi!
This is a question that I've been having troubles with.

What is the perimeter of the right triangle shown?

the left leg of the triangle is 3sqrt(2) and the bottom leg is 3sqrt(6) and I need to find the hypotenuse
in order to find the perimeter.
My fist method in finding it was to do ((3\sqrt(2))²+((3\sqrt(6))²=c² but I keep getting left to
dead ends... Any ideas on the method I should be using to get the length of the hypotenuse?

 

[ksdhart2]

Your method is absolutely the correct way to find the hypotenuse. I'm not sure what you mean by "dead ends" though, as you've not actually included any of the steps you took beyond setting up the Pythagorean Theorem. We can't "troubleshoot" work we can't see, so please include all of the work you've done on this problem, even the parts you know for sure are wrong. Thank you.

 

[markl77]

Your method is absolutely the correct way to find the hypotenuse. I'm not sure what you mean by "dead ends" though, as you've not actually included any of the steps you took beyond setting up the Pythagorean Theorem. We can't "troubleshoot" work we can't see, so please include all of the work you've done on this problem, even the parts you know for sure are wrong. Thank you.

What I ended up with was 72, which is equal to c² but then when I square root it, I just get an annoying decimal number. I'm not sure what to do from there because it's definitely not supposed to be a decimal number.

 

[Otis]

... when I square root [72], I just get an annoying decimal number. I'm not sure what to do from there because it's definitely not supposed to be a decimal number.

Instead of evaluating the square roots, you need to simplify them.

To learn how, google keywords simplify radicals for lessons, video lectures, and examples.

Once you simplify the expression for side c, you'll have the perimeter as posted by Denis. That answer can itself be further simplified, as it contains a pair of like-terms (which can be combined).

 

[Otis]

sqrt(2) = 1.414213....
What makes you think there should be no decimals?

His class is working with exact expressions, instead of decimal approximations. :cool:

 

[markl77]

Sqrt(72) = sqrt(36 * 2) = 6sqrt(2).
sqrt(2) = 1.414213....
What makes you think there should be no decimals?

Perimeter is: 3sqrt(2) + 3sqrt(6) + 6sqrt(2)

Thankyou, this helped a lot. I'm not sure what I was confused with now that I look at it again actually.