Triangle Conditions - Grade 7

A

Audentes

Junior Member
Joined
Jun 8, 2020
Messages
187
Hello, I 'm new here, I'm hoping someone can help me with a problem I got wrong. I don't understand why I got it wrong

the question is: How many integer values of x are there so that x, 12,and 9 could be the lengths of the sides of a triangle?

I know that the two smaller sides need to equal more than the greatest side, but how can I find the number of values?

Thank you!
 
You need the longest side to be less than the sum of the smallest sides
You want the longest side to be greater than the difference of the smaller sides.

There are two cases to consider. 12 is the longest side or x is the longest side.

You said that you got it wrong. Can we please your work? Maybe your method is fine but you made a silly mistake. So instead of someone here showing you how they would do it I think (and so do the other helpers here) that is best for you to show us your help. So please post back.
 
Flo Rida said:
the question is: How many integer values of x are there so that x, 12,and 9 could be the lengths of the sides of a triangle?
I know that the two smaller sides need to equal more than the greatest side, but how can I find the number of values?
Click to expand...
Actually the triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater that the third aide.
Thus:
\(12+9>x\\12+x>9\\9+x>12\)
 
Jomo said:
You need the longest side to be less than the sum of the smallest sides
You want the longest side to be greater than the difference of the smaller sides.

There are two cases to consider. 12 is the longest side or x is the longest side.

You said that you got it wrong. Can we please your work? Maybe your method is fine but you made a silly mistake. So instead of someone here showing you how they would do it I think (and so do the other helpers here) that is best for you to show us your help. So please post back.
Click to expand...
Hi thanks for getting back to me. My work was:

if 12 is the longest side, x can be 4,5,6,7,8,9,10,11,and 12. If x is the longest side, it can be greater than or equal to 9, but less than 21. I think that Imay have disregarded the second part and did not think of it as perhaps a compound inequality.
pka said:
Actually the triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater that the third aide.
Thus:
\(12+9>x\\12+x>9\\9+x>12\)
Click to expand...
Thanks for getting back to me. So I looked at the values that could be subsituted for x so that it fits all of those equations and I got:
4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,and 20. So 17 integer values?
 
You must log in or register to reply here.
Top