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som dutt
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Asked: 2023-03-28T03:46:46+00:00 In:

Show that in a right angled triangle, the hypotenuse is the longest side.

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Show that in a right angled triangle, the hypotenuse is the longest side.

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.

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      Show that in a right angled triangle, the hypotenuse is the longest side.

      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.

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