Question

Find the range for the measure of the third side of a triangle when the measures of the other two sides are 13 in. And 27 in.

Answer 1

The range for the measure of the third side of the triangle when the measures of the other two sides are 13 in. and 27 in. is x > 14.

Step-by-step explanation:

The question asks for the range of the measure of the third side of a triangle when the measures of the other two sides are 13 in. and 27 in. To find the range, 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.

In this case, let's call the third side of the triangle x. So we have two inequalities:

13 + x > 27

27 + x > 13

Solving these inequalities, we can find the range of x:

x > 14

x > -40

Therefore, the range for the measure of the third side of the triangle is x > 14.

Answer 2

Answer: The measure of the third side of a triangle, when the measures of the other two sides are 13 in and 27 in, must be greater than the difference between the measures of the other two sides (which is 27 in - 13 in = 14 in) and less than the sum of the measures of the other two sides (which is 27 in + 13 in = 40 in).

This is because according to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So the measure of the third side must be between the difference of the two given sides and the sum of the two given sides.

Therefore the range of the measure of the third side of a triangle with side lengths 13 in and 27 in is:

(14 in < x < 40 in)

or

[x > 14 in and x < 40 in].

It is also important to note that any value of x within this range will produce a valid triangle, however any value less than 14 in or greater than 40 in will not.

Step-by-step explanation: