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