Answer:-10m,11m,15m→ Not a right triangle
15m,8m,17m→ Right triangle
Explanation:-
We know that according to Pythagoras theorem of right triangles
[tex](longest\ side)^2=\text{sum of squares of remaining sides}[/tex]
Set 1. 10m,11m,15m
Let triangle with side lengths 10m,11m,15m is a right angle.
then by Pythagoras theorem
[tex]15^2=11^2+10^2\\\Rightarrow225=121+100\\\Rightarrow225=221 ,....which\ is\ not\ true.[/tex]
⇒10m,11m,15m→ Not a right triangle
Set 2. 15m,8m,17m
Let triangle with side lengths 10m,11m,15m is a right angle.
then by Pythagoras theorem
[tex]17^2=15^2+8^2\\\Rightarrow289=225+64\\\Rightarrow289=289,...........which\ is\ true.[/tex]
⇒15m,8m,17m→ Right triangle
