Question

4. Decide if the segment lengths form a triangle. If they do, Indicate whether the triangle is acute, right, or obtuse.
(a) 16, 30, 34 ? (b) 4, 5, 6?
(c) 7, 24, 26? (d) 14, 21 , 36?
can you guys tell me how to do this plz

Answer 1

Hi nisa :)

How are you?

Answer 2

Three line segments cannot form a triangle if two of the line segments sum to a value less than the third. Otherwise, they can form triangle.

Three line segments form a right triangle if and only if their three sides \(a\), \(b\), and \(c\) satisfy \(a^2+b^2\color{red}=c^2\) where \(c\) is the longest side.

Three line segments form an acute triangle if and only if their three sides \(a\), \(b\), and \(c\) satisfy \(a^2+b^2\color{red}>c^2\) where \(c\) is the longest side.

Three line segments form an obtuse triangle if and only if their three sides \(a\), \(b\), and \(c\) satisfy \(a^2+b^2\color{red}<c^2\) where \(c\) is the longest side.

Answer 3

In order to check that these are triangle you should use, this concept,

each length must be < the sum of other two.

If above condition is true then that would be the triangle otherwise not.

Answer 4

yakeyglee's post is in detail. read it carefully.

Answer 5

a+b>c, a+c>b, and b+c>a. what is this for then? i saw this on wiki it has to

Answer 6

be squared

Answer 7

That's to check if they can form a triangle.

Answer 8

a+b>c

means sum of a and b should be greater than c

Answer 9

The ones with the squared values tell you what type of triangle they are...not that they can form a triangle in the first place. Read my post very carefully!

Answer 10

i did but how exactly should i do this should i plug the three numbers in

Answer 11

Yes.

Answer 12

so 16 + 30 add up to 46 thats nore than 34 thats a triangle then right

Answer 13

yes yes. right..

Answer 14

and then i would do a^2+b^2=c^2 right

Answer 15

You would see which of the cases is true.\[a^2+b^2\color{red}=c^2\]\[a^2+b^2\color{red}>c^2\]\[a^2+b^2\color{red}<c^2\]

Answer 16

and then from that we figure out what it is

Answer 17

thankz guys :)

Answer 18

omg thanks again guys ieel so good knowing i can do it myself now lol i appreciate it alot :D

Answer 19

feel*

Answer 20

I'm glad!

Answer 21

Out of curiosity, what if you have a set of segments, say, I dunno, 7, 9, and 16? The sum of 7 and 9 is 16, and the longest side is 16; what conclusion should I make then?