the lengths of 2 sides of a triangle are 8 ft and 12 ft. find the range of possible lengths for the third side
In order for a triangle to be valid, the sum of the lengths of any two sides must be greater than the length of the remaining side.
Let's assume the length of the third side is x ft. According to the triangle inequality theorem, we have:
8 + x > 12
12 + x > 8
8 + 12 > x
Simplifying these inequalities, we get:
x > 4
x > -4
20 > x
Hence, the range of possible lengths for the third side of the triangle is 4 ft < x < 20 ft.