The triangle (a) is the right angled triangle. Option (a) is correct.
Further explanation:
The Pythagorean formula can be expressed as,
[tex]\boxed{{H^2} = {P^2} + {B^2}}.[/tex]
Here, H represents the hypotenuse, P represents the perpendicular and B represents the base.
Given:
Explanation:
In triangle (a),
The hypotenuse is [tex]\sqrt {13}[/tex]
The base is 3.
The perpendicular is 2.
Use the Pythagorean Theorem in triangle (a),
[tex]\begin{aligned}{2^2} + {3^2} &= {\left( {\sqrt {13} } \right)^2}\\4 + 9 &= 13\\13 &=13\\\end{aligned}[/tex]
Triangle (a) is right angled.
In triangle (b),
The hypotenuse is 5.
The base is [tex]3\sqrt 2.[/tex]
The perpendicular is 2.
Use the Pythagorean Theorem in triangle (b),
[tex]\begin{aligned}{2^2} + {\left( {3\sqrt 2 } \right)^2} &= {5^2}\\4 + 18&= 25\\ 22 &\ne 25\\\end{aligned}[/tex]
Triangle (b) is not right angled.
In triangle (c),
The hypotenuse is [tex]\sqrt {43}.[/tex]
The base is [tex]3\sqrt 3.[/tex]
The perpendicular is 2.
Use the Pythagorean Theorem in triangle (b),
[tex]\begin{aligned}{2^2} + {\left( {3\sqrt 3 } \right)^2}&= {\left( {\sqrt {43} } \right)^2}\\4 + 27 &= 43\\31 &\ne 43\\\end{aligned}[/tex]
Triangle (c) is not right angled.
The triangle (a) is the right angled triangle. Option (a) is correct.
Learn more:
- Learn more about inverse of the functionhttps://brainly.com/question/1632445.
- Learn more about equation of circle brainly.com/question/1506955.
- Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Triangles
Keywords: triangles, right angled triangle, Pythagoras Theorem, perpendicular, base, hypotenuse.
