Question

can the sides of a triangle have lengths 1, 5, and 1? yes no

Explanation:

Step1: Recall triangle inequality theorem

For sides $a,b,c$, $a+b>c$, $a+c>b$, $b+c>a$ must hold.

Step2: Test the given side lengths

Given sides $1, 1, \sqrt{2}$:

• $1+1>\sqrt{2}$: $2>\sqrt{2}$ (true, since $\sqrt{2}\approx1.414$)
• $1+\sqrt{2}>1$: $\sqrt{2}>0$ (true)
• $1+\sqrt{2}>1$: $\sqrt{2}>0$ (true)

All inequalities are satisfied.

Answer:

yes