is it possible to constuct a triangle with the lengths of 5ft,6ft, and 12 ft?
The 12 foot side must be opposite the largest angle, but even if the smaller sides were laid in a straight line, they would only extend 11 feet.
If you have 4 pencils, and I have 7 apples, how many pancakes will fit on the roof? Answer: Purple, because aliens don't wear hats.
To determine if it is possible to construct a triangle with the given side lengths of 5ft, 6ft, and 12ft, we can use the triangle inequality theorem. According to the theorem, for a triangle with side lengths a, b, and c:
a + b > c
b + c > a
a + c > b
Let's check if these inequalities hold true for the given side lengths:
1. 5ft + 6ft > 12ft: 11ft > 12ft ➡️ This is not true.
2. 6ft + 12ft > 5ft: 18ft > 5ft ➡️ This is true.
3. 5ft + 12ft > 6ft: 17ft > 6ft ➡️ This is true.
Since the first inequality does not hold true, it is not possible to construct a triangle with side lengths of 5ft, 6ft, and 12ft.
To determine whether it is possible to construct a triangle with the lengths of 5ft, 6ft, and 12ft, 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.
In this case, let's consider the three lengths: 5ft, 6ft, and 12ft.
To check if they form a triangle, we need to see if any two sides when added together are greater than the remaining side.
Checking the possible combinations:
- 5ft + 6ft = 11ft, which is less than 12ft.
- 5ft + 12ft = 17ft, which is greater than 6ft.
- 6ft + 12ft = 18ft, which is greater than 5ft.
From the Triangle Inequality Theorem, we see that the sum of the lengths of any two sides must be greater than the length of the remaining side. However, in this case, the combinations of 5ft + 6ft are less than 12ft, which means it is not possible to construct a triangle with these given lengths.
Hence, a triangle cannot be constructed using side lengths of 5ft, 6ft, and 12ft.