Question

Can the sides 10, 40, 42 be a right triangle?

Answer 1

The following numbers do not form a Pythagorean triplet.

Explanation:

Let the three sides be denoted as: `a,b,c` ,in which `color(blue)(a)> color(green)(b,c` .

If the sides form a Pythagorean triplet they should satisfy the Pythagoras theorem:

`color(blue)(a^2) = color(green)(b^2 +c^2`

Here `color(blue)(a=42, color(green)(b = 40, c=10`

As per theorem:

`color(blue)(a^2` should be equal to `color(green)( b^2 +c^2`

But the sum doesn't follow the Pythagoras theorem, as:

`42^2 != 40^2 + 10^2`
`1764 != 1600+ 100`
`1764!=1700`

So, the following numbers do not form a Pythagorean triplet.