Two sides of an obtuse triangle have lengths 7 and 3. If the third side is also an integer, what are its possible lengths?
If we set a=7 and b=3 then the third side must be c
We need you satisfy the following three conditions when assigning values of c
a+b>c
a+c>b
b+c>a
I will give you two solutions and let you generate the rest...
since we have a=7 and b=3 then from condition 1, a+b>c we know that c can not be bigger than 10 (and since it is an integer answer) the largest thing c can be is 9.
Using condition 1 again let's check 8. If we let c = 8 then condition 2 and 3 are still met
condition 2... a+c>b that is, 7 + 8 > 3
condition ... b + c >a that is 3 + 8 >7
your turn...
PS... this is known as the "Triangle Inequality Theorem "
To find the possible lengths of the third side of the obtuse triangle, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's denote the lengths of the sides of the triangle as A, B, and C, where C is the unknown side we are trying to find. In this case, we know that A = 7 and B = 3.
To determine the possible lengths of C, we need to check the two conditions given by the triangle inequality theorem:
1. A + B > C
7 + 3 > C
10 > C
2. A + C > B
7 + C > 3
C > -4
From these conditions, we can conclude that the possible lengths of the third side, C, can be any integer greater than -4 and less than 10. In other words, C can take any value between -3 and 9 (excluding -4 and 10).