Question

For each of the following, determine whether the given numbers represent lengths of sides of a right triangle:

a. (3/2), (4/2), (5/2)
b. sqrt 2, sqrt 3, sqrt 5
c. 18, 24, 30

Answer 1

Hint:
add the sum of squares of the two \(shorter\) sides. If the sum equals the square of the longest side, the lengths represent the sides of a right triangle.
For examle:
for sides {5,12,13},
\(5^2+12^2=25+144=169=13^2\), so {5,12,13} represent the sides of a right triangle.

Answer 2

so it would be no for all of them?

Answer 3

Yes for all of them.
Refer to the Mathematica attachment.

Answer 4

Thank you

Answer 5

Your welcome.

Answer 6

@lilmisssamy_18
I have the impression that there is a miscommunication between you and @robtobey.
Rob had shown you one of the examples, and I am not sure if you read it.
The best way to prepare yourself for this kind of question is to work them out, as I have done in the example.
For example, for (a)
\((3/2)^2+(4/2)^2=9/4+16/4=25/4=(5/2)^2\) which shows that the that lengths in (a) represent the sides of a right triangle. You just have to do the same for (b) and (c) to find the complete answer.
Remember that the question asks "for each of the case below", so you need to work out all three cases.