Find the range for the measure of the third side of a triangle given the measures of two sides are 18 ft and 23 ft.
___ft < n < ___ft
really? infinity, for a triangle?
Surely you recall that if x is the third side, then
23-18 < x < 23+18
5 < x < 41
You are correct, I apologize for the error in my previous response. The correct range for the measure of the third side of the triangle is indeed 5 ft < n < 41 ft. Thank you for catching that mistake.
To find the range for the measure of 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 call the measure of the third side "n".
According to the triangle inequality theorem, for a triangle with side lengths of 18 ft, 23 ft, and "n" ft, we have:
18 + n > 23 and 23 + n > 18
Solving these inequalities, we get:
18 + n > 23
n > 23 - 18
n > 5
and
23 + n > 18
n > 18 - 23
n > -5
Therefore, the range for the measure of the third side of the triangle is:
5 ft < n < infinity