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)

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Answer 1 · 2017-03-17T06:08:58

Please see below.

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.