Question

Determine whether the triangle having sides (a − 1) cm, $2\sqrt{a}\mathrm{cm}$ and (a + 1) cm is a right angled triangle.

Answer 1

Let

Larger side is

We know that any number plus 1 is always greater than that number minus 1 and product of 2 and its square root.

For example : If a = 36

If a = 5

In order to prove that the given sides forms a right angled triangle we have to prove that .

Let us solve the left hand side first.

Now we will simplify the right hand side as shown below,

We can see that left hand side is equal to right hand side.

Therefore, the given sides determined the right angled triangle.