Question

applications of constructions practice
complete this assessment to review what youve learned. it will not count toward your grade.
a student wants to construct a triangle with sides measuring 6 cm, 10 cm, and 16 cm. use the triangle inequality theorem to explain if this construction is possible. (1 point)
○ because 6 + 10 = 16, so the sides can form a triangle
○ because 6 + 10 = 16, not greater, so the sides cannot form a triangle
○ because 6 + 16 > 10, so the sides can form a triangle
○ because all three sides are different lengths
check answer remaining attempts 3

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 - length combinations

For sides \(a = 6\mathrm{cm}\), \(b = 10\mathrm{cm}\), and \(c = 16\mathrm{cm}\), we check \(a + b\), \(a + c\), and \(b + c\).
\(a + b=6 + 10=16\), but the triangle - inequality requires \(a + b>c\). Here \(a + b = c\) (where \(c = 16\)), not \(a + b>c\).

Answer:

Because \(6 + 10 = 16\), not greater, so the sides cannot form a triangle.