Statement 1: The sides of a triangle are of length 6 cm, 4.5 cm and 7.5 cm. The angle opposite to the side 7.5 cm is 90°.
Statement 2: A triangle having one right angle is called a right-angled triangle.
Which of the following options is correct?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Answer
Here the longest side is 7.5 cm.
(7.5)2 = 7.5 × 7.5 = 56.25
(4.5)2 + 62 = 20.25 + 36 = 56.25
Since (7.5)2 = (4.5)2 + 62, Pythagoras theorem holds, so the angle opposite the longest side 7.5 cm is 90°. Thus, statement 1 is true.
A triangle having one right angle is called a right-angled triangle. Thus, statement 2 is true.
Hence, option 1 is the correct option.
Statement 1: A right angled triangle may be an isosceles triangle.
Statement 2: Vertex angle of a right angled isosceles triangle is 90°.
Which of the following options is correct?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Answer
A right-angled triangle may be an isosceles triangle, because a triangle can have a right angle and, at the same time, two equal sides (an isosceles right-angled triangle).
Thus, statement 1 is true.
In a right-angled isosceles triangle, the two equal sides contain the right angle, so the vertex angle (the angle between the two equal sides) is 90°.
Thus, statement 2 is true.
Hence, option 1 is the correct option.