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Two sides of an obtuse triangle have lengths 7 and 3. If the third side is also an integer, what are its possible lengths?smiley

 Apr 25, 2018
 #1
avatar+985 
+3

Using the rule about the sides of a triangle, where the sum of any two sides must be greather than the third. 

 

We have these inequalities:

 

7 + 3 > x

 

7 + x > 3

 

x + 3 > 7

 

Simplifying these inequalities, we have:

 

x < 10

 

x > -4

 

x > 4

 

The possible integer lengths are:

 

5, 6, 7, 8, and 9.

 

I hope this helped, 

 

Gavin.

 Apr 25, 2018
 #2
avatar+4286 
+2

Solution:

a^2+b^2=c^2

So, 7^2+3^2=c^2

m^2=58

m=7.61- 8

7+3>m

m<10

So, 5,6,7,,8,9

 Apr 25, 2018

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