Is a triangle with sides of 3,4,6 a right triangle?

Does #3^2+4^2# equal #6^2#?

#3^2+4^2stackrel?=6^2#

#9+16stackrel?=36#

#25!=36#

Since #25# isn't #36# the triangle is not a right triangle.

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We are given three sides of a triangle #3, 4 and 6#.

Pythagoras Theorem states that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

To determine whether the three given sides form a right triangle, we use the Pythagoras Theorem to verify.

Draw a triangle, say #A, B, C# with the given magnitudes.

Note that the longest side (BC) has a magnitude of #6# units.

Hence, this must be the Hypotenuse, if triangle ABC is a right-triangle.

Does the angle #/_ CAB# make a right angle of #90^@#?

Verify that using the relationship between the hypotenuse and the other two legs of the triangle.

If #(AB)^2 + (AC)^2 = (BC)^2#, then we know that #BC# is the Hypotenuse and the triangle #ABC# is a right-triangle.

#bar (AB)=3#; #bar (AC) = 4#; and #bar (BC) = 6#

#(AB)^2 = 9#

#(AC)^2 = 16#

#(BC)^2 = 36#

#(AB)^2 + (AC)^2 = 9+16=25#

Hence,

#(AB)^2 + (AC)^2 != (BC)^2#

Hope it helps.