Given below are two statements: Statement I: If you know the length of two…
2020
Given below are two statements:
Statement I: If you know the length of two sides of a right angled triangle then the length of the third side cannot be found.
Statement II: The internal angles of a triangle add upto 180°.
In the light of the above statements, choose the correct answer from the options given below:
- A.
Both Statement I and Statement II are true.
- B.
Both Statement I and Statement II are false.
- C.
Statement I is correct but Statement II is false.
- D.
Statement I is incorrect but Statement II is true.
Show answer & explanation
Correct answer: D
Concept
Two elementary facts of plane triangles govern this item. First, in a right-angled triangle the Pythagorean theorem links the three sides as a2 + b2 = c2, where c is the hypotenuse; this single relation determines any one side once the other two are known. Second, the angle-sum property states that the three interior angles of every triangle total 180°.
Applying it to each statement
Statement I claims the third side cannot be found from two known sides of a right triangle. The Pythagorean relation gives the third side directly: a missing leg is √(c2 − a2) and a missing hypotenuse is √(a2 + b2). So the third side certainly can be found, and Statement I is false.
Statement II asserts the interior angles sum to 180°. This is the standard angle-sum theorem for any triangle, so Statement II is true.
Cross-check and result
Concretely, legs 3 and 4 give a hypotenuse √(32 + 42) = 5, confirming the third side is recoverable, while drawing any triangle and measuring its angles confirms the 180° total. Hence Statement I is incorrect and Statement II is true.