Question

A triangle has sides with lengths of 14 yards 17 yards and 18 yard is it a right triangle yes or no

Answer 1

The given sides of the triangle are : 14 yards, 17 yards & 18 yards.

Condition of a right angle triangle :

1) The sum of square of Base and the perpendicular sides of traingle are always equal to the square of Hypotenuse.

Hypotenuse² = Perpendicular² + Base²

where, Hypotenuse, Base and perpendicular are express as :

2) The hypotenuse side of the right angle triangle is always the longest side.

In the given sides of triangle :

18 is the longest one, consider 18 as the Hypotenuse and remaing as the perpendicular and base

i.e.

Hypotenuse = 18, Base = 17 and perpendicular = 14

Substitute the value in the expression of the second condition :

Hypotenuse² = Perpendicular² + Base²

18² = 14² + 17²

324 = 196 + 289

324 = 485

LHS is not equal to RHS

Thus, expression doesnot hold

Hence the given sides of triangle is not a right angle triangle

Answer : The given sides of triangle is not a right angle triangle