Question

It is possible to have a right-angled equilateral triangle. State whether the statement is True or False.

• A. True
• B. False

Answer 1

The correct option is B False

Find whether the given statement is True or False

A right-angled triangle has three sides: hypotenuse, perpendicular and base. The base, and the perpendicular, make an angle of $90°$ with each other. So, Pythagoras theorem states that “the square of the hypotenuse is equal to the sum of base square and perpendicular square”.

But, we know that in an equilateral triangle, all sides are always equal. Therefore, all angles are also equal.

We know that the sum of all three angles of any triangle is equal to $180°$

So, each angle of an equilateral triangle $=\frac{180°}{3}=60°$.

Hence, it is proved that a right-angled equilateral triangle is impossible.

Hence, the given statement is False.