Suppose you have three sticks of lengths 10 cm, 20 cm, and 31 cm. Can you arrange these sticks into a triangle? If not, why not?
no,
the sum of any two sides of a triangle must be larger than the third side
10 + 20 is not greater than 31
To determine whether these sticks can be arranged into a triangle, we can use the Triangle Inequality Theorem. According to this theorem, for a triangle to be formed, the sum of the lengths of any two sides must be greater than the length of the remaining side.
Let's check if this holds true for the given lengths:
1. The first stick has a length of 10 cm.
2. The second stick has a length of 20 cm.
3. The third stick has a length of 31 cm.
Now, we need to check whether the sum of any two sides is greater than the remaining side:
1. Sum of the first two sticks: 10 + 20 = 30 cm
Is 30 cm greater than the length of the third stick (31 cm)? No.
Therefore, we cannot arrange these sticks into a triangle. The sum of the lengths of the two smaller sticks (10 cm and 20 cm) is not greater than the length of the largest stick (31 cm), violating the Triangle Inequality Theorem.