Mehreen F.

asked • 02/22/13

If the right angled triangle t, with sides of length a and b and hypotenuse of length c, has area equal to c^2/4, then t is an isosceles triangle.

discrete math

Bhadra P.

Given: Angle t is right angle, a = b , 

Since t is Rt angle, side a is perpendicular to side b or equivalent to height

Therefore, area (A) = 1/2 a. b =  1/2 a^2 or 1/2 b^2 ...   ....    ....   .....     .....  (1)

Also, c^2= a^2+ b^2 = 2a^2 or 2b^2 is given for Rt angled triangle.

Therefore,  by dividing both sides by 2  we get a^2 = 1/2 c^2.   ...    ....    ... (2)

By substitution this value from (2) in (1) above, we get

A = 1/2 . 1/2 c^2 = 1/4 c^2

i hope it is clear enough.

Bhadra Panta



Jacob W.

There is the additional necessary condition that the triangle is isosceles for this explanation to be valid. The fact that there is a right triangle does not guarantee that a=b. (Note 3,4,5 right triangles for example.) The right angle simply validates the Pythagorean theorem for the area of the triangle.



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Johanna R. answered • 02/23/13

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Bhadra P. answered • 02/22/13

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Jacob W. answered • 02/22/13

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