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 Triangle Question

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In triangle ABC, the length of each side is measured by an integer number of centimeters. If the AB side is 14 cm longer than the AC, and BC is 30 cm longer than AC, the minimum possible value for the perimeter, in cm, of the triangle is:?

 Nov 27, 2015

Best Answer 

 #4
avatar+286 
+6

Thanks havn't learned this rule set yet, but still thank you! laugh

 Nov 27, 2015

4+0 Answers

 #1
avatar+129958 
+7

AB = AC + 14

 

BC  = AC + 30

 

And by the triangle inequality :

 

AB + AC > BC

 

[AC + 14] + AC > AC + 30

 

2AC + 14 > AC + 30

 

AC > 16

 

Which means that AB > 30     and BC > 46

 

Then, the minimum perimeter must be something greater than 16 + 30 + 46  = 92 cm

 

 

cool cool cool

 Nov 27, 2015
 #2
avatar+286 
+6

I understand, but in my answear sheet i don't have 92 the closest i get is 95, 94 and 91!

 Nov 27, 2015
 #3
avatar+129958 
+6

Well.....buubleman......I see that since each side must be an integer quantity and AC > 16......the next integer would be 17

 

So  AB would be 14 more than this = 31

 

And BC would be 30 more = 47

 

So........ 17 + 31 + 47 =   95

 

 

cool cool cool

 Nov 27, 2015
 #4
avatar+286 
+6
Best Answer

Thanks havn't learned this rule set yet, but still thank you! laugh

buubleman Nov 27, 2015

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