Show that the triangle of side 5,11and 12is not right angle triangle?? ?

To show that the triangle with sides 5, 11, and 12 is not a right angle triangle, we can use the Pythagorean theorem.

In a right angle triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

Let's calculate the squares of the sides:
5^2 = 25
11^2 = 121
12^2 = 144

Now, let's check if the Pythagorean theorem holds true for this triangle:
25 + 121 = 146

Since 146 is not equal to 144, the triangle with sides 5, 11, and 12 is not a right angle triangle.

Using Heron's Formula:

Heron's formula states that the area of a triangle with sides a, b, and c is given by:

```
Area = √(s(s-a)(s-b)(s-c))
```

where s is the semi-perimeter of the triangle, which is given by:

```
s = (a + b + c) / 2
```

For a right-angled triangle, the area should be half the product of the two shorter sides.

Calculating the area:

For the given triangle with sides 5, 11, and 12:

```
s = (5 + 11 + 12) / 2 = 14
```

```
Area = √(14(14-5)(14-11)(14-12)) = 30
```

Checking the condition:

Half the product of the two shorter sides is:

```
(5 - 11) / 2 = 27.5
```

Since the calculated area (30) is not equal to half the product of the two shorter sides (27.5), the given triangle is not a right-angled triangle.