Question

1. can you make a triangle given the following sides? if yes, classify the triangle as scalene, isosceles or equilateral. if no, write

ot a triangle\ a) 5,5,5 b) 23,10,13 c) 11,6,6

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: Analyze part a

For side - lengths 5, 5, 5:
$5 + 5>5$, $5+5 > 5$, and $5 + 5>5$. Since all sides are equal, it is an equilateral triangle.

Step3: Analyze part b

For side - lengths 23, 10, 13:
$10 + 13=23$, which does not satisfy the triangle - inequality theorem. So, it is not a triangle.

Step4: Analyze part c

For side - lengths 11, 6, 6:
$6+6 = 12>11$, $6 + 11>6$, and $11+6>6$. Since two sides are equal, it is an isosceles triangle.

Answer:

a) equilateral
b) not a triangle
c) isosceles