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

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Answer 1 · 2015-07-01T08:28:17

The following numbers do not form a Pythagorean triplet.

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.