the lengths of 2 sides of a triangle are 8 ft and 12 ft. find the range of possible lengths for the third side
a. 8<x<12
b. 0<x<12
c. 8<x<72
d. 4<x<20
To find the range of possible lengths for the third side of a triangle, we can use the triangle inequality theorem, which states that 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 as follows:
Side 1: a = 8 ft
Side 2: b = 12 ft
Side 3: x (unknown)
According to the inequality theorem:
a + b > x
8 + 12 > x
20 > x
Also, the difference between the lengths of any two sides of a triangle must be less than the length of the third side:
|a - b| < x
|8 - 12| < x
4 < x
Combining both inequalities, we have:
4 < x < 20
Therefore, the range of possible lengths for the third side is 4 < x < 20.
The correct answer is:
d. 4 < x < 20