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The given lengths are: 24, 30, 6 square root of 41, do they represent the sides of a right triangle?

Answer 1

Yes.

To find out if these are the sides of a right triangle, we will check if the square root of the sum of the squares of the two shorter sides is equal to the longest side. We're going to make use of the Pythagorean theorem:

#c=sqrt(a^2+b^2)#; where #c# is the longest side (hypotenuse)

Okay, let's start by checking which are the two shorter lengths. These are 24 and 30 (because #6sqrt41# is around 38.5). We'll substitute 24 and 30 into #a# and #b#.

#c=sqrt(a^2+b^2)# #c=sqrt(24^2+30^2)# #c=sqrt(576+900)# #c=sqrt(1476)# #c=sqrt(6^2*41)# #color(red)(c=6sqrt(41))#

Since #c=6sqrt41#, then the three lengths represent the sides of a right triangle.

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Answer 2

Avery Alexander

Yes, the given lengths represent the sides of a right triangle.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.