Question

Sides of the triangle are $7$ $cm$, $24$ $cm$ and $25$ $cm$. Determine whether the triangle is right-angled triangle or not.

Answer 1

Let $a=7$ $cm$, $b=24$ $cm$ and $c=25$ $cm$.

Then, length of longest side, $c=25$ $cm$.

$\therefore c^2={25}^2=625$

and $a^2+b^2={\left(7\right)}^2+{\left(24\right)}^2=49+576=625$

$\therefore c^2=a^2+b^2$

i.e. ${\left(25\right)}^2={\left(7\right)}^2+{\left(24\right)}^2$

$\therefore$ by the Pythagoras theorem, these are the sides of a right angled triangle.