Question

For a right-angled triangle with sides $a$, $b$ and $c$, the following equation for the area of squares drawn on the sides always holds true:
$a^2=b^2+c^2$

• A. True
• B. False

Answer 1

The correct option is B False

For a right angled $△ABC$, if $BC$ is the $hypotenuse$ and $a,b,c$ are sides opposite to$\angle A,\angle B,\angle C$ respectively, then by Pythagoras Theorem,

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

If we draw squares on sides of the triangle, with each side forming the base of the square, then the area of the square on the hypotenuse is equal to sum of the area of the squares on the other two sides.

This is nothing but the Pythagoras theorem itself.

Pythagoras theorem is always true for a right-angled triangle. Hence, this is always true either.

But in the question which sides correspond to the base, hypotenuse and height are not specified so the doesn't always hold true.