If 2 side lengths of a triangle are 5ft and 8ft what could the third side length NOT be? Choices: 4ft, 8ft, 11ft or 15ft.
If the 3rd side is x, then
8-5 < x < 8+5
third side ---- x
x + 5 > 8
x > 3
AND
x + 8 > 5
x > -3 , of course
AND
5 + 8 > x
x < 13
so 3 < x < 13
Now you decide ....
To determine the possible lengths of the third side of a triangle given the lengths of the other two sides, you can use the triangle inequality theorem. According to the triangle inequality theorem, the sum of any two side lengths of a triangle must be greater than the length of the third side.
In this case, the two given side lengths are 5ft and 8ft. Let's go through each of the choices provided and check if they satisfy the triangle inequality theorem:
1. 4ft: To form a triangle, the sum of the two smaller sides must be greater than the length of the third side. In this case, 5ft + 4ft = 9ft, which is greater than 8ft. So, 4ft is a possible length for the third side.
2. 8ft: This is one of the given side lengths, so it's definitely a possible length for the third side.
3. 11ft: Using the triangle inequality theorem, we check if 5ft + 11ft > 8ft and 8ft + 11ft > 5ft. However, 8ft + 11ft = 19ft, which is not greater than 5ft. Therefore, 11ft is NOT a possible length for the third side.
4. 15ft: Again, we need to check if 5ft + 15ft > 8ft and 8ft + 15ft > 5ft. However, 8ft + 15ft = 23ft, which is greater than both 5ft and 8ft. Thus, 15ft is a possible length for the third side.
In conclusion, the third side of the triangle could NOT have a length of 11ft.