Question

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Answer 1

Answer:

This is not a Right angled triangle.

Step-by-step explanation:

In a right angled triangle , sum of square of two sides is equal to square of third side.

The squares of the sides of triangle are

(a-1)²=a²-2a+1

(a+1)²=a²+2a+1

(2√2a)²=8a².

Adding any two side squares of these doesn't give the square of the third side, so this is not a right angled triangle.

Answer 2

Information provided to us:

First side = ( a - 1 ) cm
Second side = ( 2√2 a ) or ( 2a√2 ) cm
Third side = ( a + 1 ) cm

We know that in a right-angled triangle the sum of the squares of two sides containing the right angle is equal to the square of the hypotenuse.

Since we do not know which side is the hypotenuse, we will use hit and trial method.

Let us calculate the squares of each side:
Square of first side = ( a - 1 ) ^ 2 = a ^ 2 + 1 - 2a
Square of second side = ( 2a √2 ) ^ 2 = 8a ^ 2
Square of third side = ( a + 1 ) ^ 2 = a ^ 2 + 1 + 2a

Now we can easily find that adding any of the two side does not give the third side so we can conclude that this triangle cannot be a right-angled triangle.