Which is Acute,Obtuse, and Right?(3, 5,and 7)(4.5, 6, and 7.5)(6, 8, and 9)(1.2, 2.5, and 3.1)(8, 15, and 17)(14, 19, and 21)

1 Answer
Mar 17, 2017

Please see below.

Explanation:

Although it has not been clearly mentioned, it appears that questioner has given the lengths of sides of #color(red)"six"# triangles.

Let these be

#DeltaA-(3, 5, 7)#
#DeltaB-(4.5, 6, 7.5)#
#DeltaC-(6, 8, 9)#
#DeltaD-(1.2, 2.5, 3.1)#
#DeltaE-(8, 15, 17)#
#DeltaF-(14, 19, 21)#

In a right angled triangle say #Delta-(P,Q,R)#, if #R# is the largest side, then #R^2=P^2+Q^2#.

In an acute angled triangle say #Delta-(P,Q,R)#, if #R# is the largest side, then #R^2 < P^2+Q^2#.

In an obtuse angled triangle say #Delta-(P,Q,R)#, if #R# is the largest side, then #R^2 > P^2+Q^2#.

Hence as #7^2 > 3^2+5^2#, #DeltaA# is obtuse angled triangle.

As #7.5^2 = 4.5^2+6^2#, #DeltaB# is right angled triangle.

As #9^2 < 6^2+8^2#, #DeltaC# is acute angled triangle.

As #3.1^2 > 1.2^2+2.5^2#, #DeltaD# is obtuse angled triangle.

As #17^2 = 8^2+15^2#, #DeltaE# is right angled triangle.

As #21^2 > 9^2+14^2#, #DeltaF# is obtuse angled triangle.