which of the following can be the sides of a right triangle?
i) 2.5 cm, 6.5 cm, 6cm.
ii) 2 cm, 2cm, 5cm.
iii) 1.5cm, 2.5cm, 2cm.
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Answers
Answer:
As we know,
In a Right-angled Triangle: By Pythagoras Theorem,
(Hypotenus)^2=(Base)^2+(Perpendicular)^2
(i) \small 2.5\hspace{1mm} cm, \small 6.5\hspace{1mm} cm, 6 cm.
As we know the hypotenuse is the longest side of the triangle, So
Hypotenuse = 6.5 cm
Verifying the Pythagoras theorem,
(6.5)^2=(6)^2+(2.5)^2
42.25=36+6.25
42.25=42.25
Hence it is a right-angled triangle.
The Right-angle lies on the opposite of the longest side (hypotenuse) So the right angle is at the place where 2.5 cm side and 6 cm side meet.
(ii) 2 cm, 2 cm, 5 cm.
As we know the hypotenuse is the longest side of the triangle, So
Hypotenuse = 5 cm
Verifying the Pythagoras theorem,
(5)^2=(2)^2+(2)^2
25=4+4
25\neq8
Hence it is Not a right-angled triangle.
(iii) \small 1.5\hspace{1mm} cm, 2cm, \small 2.5\hspace{1mm} cm.
As we know the hypotenuse is the longest side of the triangle, So
Hypotenuse = 2.5 cm
Verifying the Pythagoras theorem,
(2.5)^2=(2)^2+(1.5)^2
6.25=4+2.25
6.25=6.25
Hence it is a Right-angled triangle.
The right angle is the point where the base and perpendicular meet.
Step-by-step explanation:
Answer:
If a triangle is Right Angle Triangle, then it should must follow Pythagorean Triplet.
1) 2.5 cm, 6.5 cm, 6 cm
⇒ h² = p² + b²
⇒ (6.5)² = (6²) + (2.5)²
⇒ 42.25 = 36 + 6.25
⇒ 42.25 = 42.25
∴ Hence, this is a Right Angle Triangle.
━━━━━━━━━━━━━━━━
2) 2 cm, 2 cm, 5 cm
⇒ h² = p² + b²
⇒ (5)² = (2²) + (2)²
⇒ 25 = 4 + 4
⇒ 25 ≠ 8
∴ Hence, this isn't a Right Angle Triangle.
━━━━━━━━━━━━━━━━
3) 1.5 cm, 2.5 cm, 2 cm
⇒ h² = p² + b²
⇒ (2.5)² = (1.5²) + (2)²
⇒ 6.25 = 2.25 + 4
⇒ 6.25 = 6.25
∴ Hence, this is a Right Angle Triangle.