Determine if it is possible to form a triangle using the set of segments with the given measurements. Explain your reasoning.
7 in., 8.7 in, 15.4 in.
Please help! Thank you!!
yes
the longest side is less than the sum of the two shorter sides
Thank you so much!
Well, let's see if we can put this puzzle together! To determine if it's possible to form a triangle, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
Now, let's apply this to the given measurements: 7 in., 8.7 in, and 15.4 in.
If we take the shortest segment, which is 7 in., we can see that the sum of 7 in. and 8.7 in. is less than 15.4 in. Therefore, we cannot form a triangle using these measurements. It's like trying to connect two friends who are very close to each other using a really long rope. It just wouldn't work!
So, the answer is a resounding "nope," unfortunately. Time to go back to the drawing board! Don't worry, though, I'm sure you'll find the right measurements for your triangle soon enough. Keep trying, and don't be triangled!
To determine if it is possible to form a triangle using the set of segments with measurements 7 in., 8.7 in., and 15.4 in., we need to check if the sum of the lengths of any two sides of the triangle is greater than the length of the third side.
Let's go step by step to check:
1. Compare the sum of the first two sides (7 in. + 8.7 in. = 15.7 in.) with the length of the third side (15.4 in.):
- Is 15.7 in. greater than 15.4 in.? Yes, it is.
2. Compare the sum of the first and third sides (7 in. + 15.4 in. = 22.4 in.) with the length of the second side (8.7 in.):
- Is 22.4 in. greater than 8.7 in.? Yes, it is.
3. Compare the sum of the second and third sides (8.7 in. + 15.4 in. = 24.1 in.) with the length of the first side (7 in.):
- Is 24.1 in. greater than 7 in.? Yes, it is.
Since for each comparison, the sum of the two shorter sides is greater than the length of the longest side, it is possible to form a triangle using the given set of segments (7 in., 8.7 in., and 15.4 in.).
Therefore, we can conclude that it is possible to form a triangle with these measurements.
To determine if it is possible to form a triangle using the given set of segments, we need to check if the sum of the lengths of any two sides is greater than the length of the third side.
Let's take each pair of sides and check this condition:
1) 7 in. and 8.7 in.
To check if these two sides can form a triangle, we calculate the sum: 7 + 8.7 = 15.7 in. Since 15.7 in is greater than the remaining side length (15.4 in), this condition is satisfied.
2) 7 in. and 15.4 in.
Calculating the sum: 7 + 15.4 = 22.4 in. As 22.4 in is greater than the remaining side length (8.7 in), this condition is satisfied as well.
3) 8.7 in. and 15.4 in.
Adding the lengths gives us: 8.7 + 15.4 = 24.1 in. As 24.1 in is greater than the remaining side length (7 in), this condition is also satisfied.
In all three cases, the sum of the lengths of any two sides is greater than the length of the third side. Therefore, it is possible to form a triangle using the given set of segments.
Note that we assumed the given measurements to be accurate, as slight measurement errors could affect the result.