A triangle has sides with lengths of 34 centimeters, 60 centimeters, and 69 centimeters. Is it a right triangle?

Nov 29, 2016

The triangle is not right triangle.

Explanation:

To check whether a triangle, formed by three sides of given length, is right triangle or not.

square of the largest side should be equal to sum of the squares of other two sides.

As ${69}^{2} = 4761$ and ${34}^{2} + {60}^{2} = 1156 + 3600 = 4756$

As $4761 \ne 4756$, the triangle is not right triangle.

Note: (1) In fact ${69}^{2} < {34}^{2} + {60}^{2}$, hence, it is acute angled triangle. (2) There was no need of squaring and adding smaller sides. As they both are even, sum of squares of smaller sides will be even and large side being of odd length, its square will be odd. Hence even without squaring one can say, that triangle is not right triangle.