Answer:
3, 14, and sqrt205.
2,9, and sqrt85.
Step-by-step explanation:
Check if they fit the Pythagoras theorem c^2 = a^2 + b^2:
3^2 = 9 , 14^2 = 196.
9 + 196 = 205 which is the square of sqrt205.
So this is a right angled triangle.
6^2 + 11^2 = 36 + 121
= 157 Not right-angled.
19^2 + 180^2 = 32761 Not right-angled.
3^2 + 19^2 = 370 Not right-angled.
2^2 + 9^2 = 85, So this is right angled..
The sides of a right angled triangle obey Pythagoras Theorem which states that the hypotenuse squared is sum of square of rest of the sides of that triangle.
Thus, only options A and E satisfy that given condition.
A right angled triangle is a triangle having one of its angle with measure of 90 degrees.
The slant side of that triangle is called Hypotenuse and it is the longest side in that triangle.
If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]AC^2 = AB^2 + BC^2[/tex]
3, 14, [tex]\sqrt{205}[/tex]
We have [tex]\sqrt{205}[/tex] as largest since evaluates around 14.31
[tex](\sqrt{205})^2=205\\\\3^2 + 14^2 = 196+9=205\\\\Thus.\\(\sqrt{205})^2 = 3^2 + 14^2[/tex]
Thus, these are sides of right angled triangle.
6,11, [tex]\sqrt{158}[/tex]
Since [tex]\sqrt{158}[/tex] evaluates around 12.56, thus it is biggest.
[tex](\sqrt{158})^2 = 158\\6^2 + 11^2 = 36 + 121 = 157\\(\sqrt{158})^2 \neq 6^2 + 11^2[/tex]
These are not sides of right angled triangle.
19,1 80, [tex]\sqrt{181}[/tex]
180 is largest side here.
[tex]180^2 = 32400\\(\sqrt{181})^2 +19^2= 181 + 361 = 542\\\text{both unequal}[/tex]
Thus, these aren't sides of right triangle.
3,19,[tex]\sqrt{380}[/tex]
[tex]\sqrt{380}[/tex] evaluates around 19.49, thus it is biggest side.
[tex](\sqrt{380})^2 = 380\\3^2 + 19^2 = 9 + 361 = 370\\(\sqrt{380})^2 \neq 3^2 + 19^2[/tex]
Thus, these sides are not of right triangle.
2, 9, [tex]\sqrt{85}[/tex]
[tex]\sqrt{85}[/tex] evaluates around 9.21 thus it is biggest.
[tex](\sqrt{85})^2 =85\\2^2 +9^2 = 85\\(\sqrt{85})^2 = 2^2 + 9^2[/tex]
These represents sides of a right angled triangle.
Thus, only option A and E are correct.
Learn more about right angled triangles here:
https://brainly.com/question/396866
