Question

The sides of certain triangle are (a - 1) cm, 2√a cm, (a+1) Determine whether the triangle is a right triangle.
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Answer 1

Answer:

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Step-by-step explanation:

Answer

AB=(a−1)cm,BC=2

a

cm,CA=(a+1)cm

Hence, AB

2

=(a−1)

2

=a

2

+1−2a

BC

2

=(2

a

)

2

=4a

AC

2

=(a+1)

2

=a

2

+1+2a

AB

2

+BC

2

=a

2

+1−2a+4a

AB

2

+BC

2

=a

2

+1+2a

∴ AC

2

=AB

2

+BC

2

So, △ABC is a right-angled triangle

Answer 2

Step-by-step explanation:

Given

Sides of triangle:

(a - 1) cm, 2√a cm, (a+1)

For the triangle to be a right-angled triangle,

It should satisfy the pythagorean theorem.

(a-1)² + (2√a)²

= a² +1 - 2a + 4a

= a² + 2a + 1

= (a+1)²

Because, (a-1)² +( 2√a)² = p²+b² = (a+1)² = h²

Hence, It is a right angled triangle.