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

Jul 1, 2015

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:

${42}^{2} \ne {40}^{2} + {10}^{2}$
$1764 \ne 1600 + 100$
$1764 \ne 1700$

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