Question

can a triangle exist with the given side measures? no yes 4, 7, 10 answer by dragging items here 14, 18, 32 answer by dragging items here 103, 41.9, 62.5 answer by dragging items here

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Step2: Check side - lengths 4, 7, 10

$4 + 7=11>10$, $4 + 10 = 14>7$, $7+10 = 17>4$. So a triangle can exist.

Step3: Check side - lengths 14, 18, 32

$14 + 18=32$, which is not greater than 32. So a triangle cannot exist.

Step4: Check side - lengths 103, 41.9, 62.5

$41.9+62.5 = 104.4>103$, $41.9 + 103=144.9>62.5$, $62.5+103 = 165.5>41.9$. So a triangle can exist.

Answer:

Yes
No
Yes