Question

Using the Pythagorean theorem which of the triangles shown are right triangles?

Answer 1

Answer:

Triangle a

Step-by-step explanation:

The Pythagorean theorem states that the sums of the squares of the two legs of a right triangle is equal to the square of the hypotenuse; algebraically,

a²+b² = c²

For triangle a, we have

2²+3² = (√13)²

4+9 = 13

This is a true statement, so triangle A is a right triangle.

For triangle B,

2²+(3√2)² = 5²

4+9(2) = 25

4+18 = 25

This is not a true statement, so triangle B is not a right triangle.

For triangle C,

2²+(3√3)² = (√43)²

4+9(3) = 43

4+27 = 43

This is not a true statement, so triangle C is not a right triangle.

Answer 2

The triangle (a) is the right angled triangle. Option (a) is correct.

Further explanation:

The Pythagorean formula can be expressed as, $\boxed{{H^2} = {P^2} + {B^2}}.$

Here, H represents the hypotenuse, P represents the perpendicular and B represents the base.

Given:

Explanation:

In triangle (a),

The hypotenuse is $\sqrt {13}$

The base is 3.

The perpendicular is 2.

Use the Pythagorean Theorem in triangle (a),

$\begin{aligned}{2^2} + {3^2} &= {\left( {\sqrt {13} } \right)^2}\\4 + 9 &= 13\\13 &=13\\\end{aligned}$

Triangle (a) is right angled.

In triangle (b),

The hypotenuse is 5.

The base is $3\sqrt 2.$

The perpendicular is 2.

Use the Pythagorean Theorem in triangle (b),

$\begin{aligned}{2^2} + {\left( {3\sqrt 2 } \right)^2} &= {5^2}\\4 + 18&= 25\\ 22 &\ne 25\\\end{aligned}$

Triangle (b) is not right angled.

In triangle (c),

The hypotenuse is $\sqrt {43}.$

The base is $3\sqrt 3.$

The perpendicular is 2.

Use the Pythagorean Theorem in triangle (b),

$\begin{aligned}{2^2} + {\left( {3\sqrt 3 } \right)^2}&= {\left( {\sqrt {43} } \right)^2}\\4 + 27 &= 43\\31 &\ne 43\\\end{aligned}$

Triangle (c) is not right angled.

The triangle (a) is the right angled triangle. Option (a) is correct.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Triangles

Keywords: triangles, right angled triangle, Pythagoras Theorem, perpendicular, base, hypotenuse.