Which of the triangles are right triangles?
Solution:
A triangle having an angle of 90° is called a right-angled triangle.
We need to make use of the Pythagoras property for the right-angled triangle.
We know that the Pythagoras theorem is satisfied only in right triangles. Pythagora property states, (Hypotenuse)2 = (Perpendicular)2 + (Base)2
Since the Pythagoras theorem holds true only in the right-angled triangle, so we can verify the above options, by putting them one by one in the Pythagoras theorem.
Option 1) (3)2 + (5)2 = 34 ≠ 35. Thus, it is not a right-angled triangle.
Option 2) (5)2 + (4)2 = 41 = 41. Thus, it is a right-angled triangle.
Option 3) (6)2 + (8)2 = 100 ≠ 10. Thus, it is not a right-angled triangle.
Option 4) (3)2 + (3)2 = 18 ≠ 27. Thus, it is not a right-angled triangle.
Hence, by the use of the Pythagoras property, we conclude that only option 2 is the right-angled triangle.
Which of the triangles are right triangles?
Summary:
By the use of the Pythagoras property, we conclude that only option 2 is the right-angled triangle.