How hypotenuse is the longest side in the right-angled triangle.
Class 9th Mathas, Page No:132, Questions No:1, Exercise 7.4
Triangles Solutions for Class 9th Maths, Session 2023-2024.
CBSE Board and Others state Board.
Show that in a right angled triangle, the hypotenuse is the longest side.
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In ΔABC ∠B = 90° [∵ Given]
Therefore, ∠A < 90° and ∠C ∠C [∵ ∠B = 90° and ∠C AB …(1) [∵ In a triangle, greater angle has longer side opposite to it]
Similarly, in Δ ABC, ∠B > ∠A [∵ ∠B = 90° and ∠A BC …(2) [∵ In a triangle, greater angle has longer side opposite to it]
From the equation (1) and (2), we have
AC > AB and AC > BC
Hence, hypotenuse AC is the longest side.