Question

Could 7.7 cm, 4.0 cm, and 1.7 cm be the side lengths of a triangle?

Answer 1

• Triangle Inequality Theorem: States that the sum of any two sides of a triangle is greater than the length of the third side; $A+B>C\\B+C>A\\A+C>B$

So for this, we are applying the triangle inequality theorem. If any of the inequalities are not true, then this cannot be a triangle. (Let A = 7.7, B = 4.0, and C = 1.7)

$7.7+4.0>1.7\\11.7>1.7\ \textsf{(true)}\\\\4.0+1.7>7.7\\5.7>7.7\ \textsf{(false)}\\\\7.7+1.7>4.0\\9.4>4.0\ \textsf{(true)}$

Since the second inequality is false, these lengths cannot form a triangle.