MATH SOLVE

4 months ago

Q:
# GeometryYou have two pieces of wood that will make up two sides of a triangular picture frame. One is 6 in. long and the other is 7 in. long. What is the range of the possible lengths of the frame?

Accepted Solution

A:

x = length of third side

The third side is unknown and can't be determined to be one fixed number. However, we can find a set of values or a range of acceptable values

If we know that

a = 6

b = 7

are the two given sides, then we can say

b-a < x < b+a

7-6 < x < 7+6

1 < x < 13

So the third side x can be between 1 and 13.

The third side cannot be equal to 1 unit or 13 units because a triangle would not form. Instead a straight line would form.

Note: This idea is using the triangle inequality theorem

The third side is unknown and can't be determined to be one fixed number. However, we can find a set of values or a range of acceptable values

If we know that

a = 6

b = 7

are the two given sides, then we can say

b-a < x < b+a

7-6 < x < 7+6

1 < x < 13

So the third side x can be between 1 and 13.

The third side cannot be equal to 1 unit or 13 units because a triangle would not form. Instead a straight line would form.

Note: This idea is using the triangle inequality theorem